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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 2753659, 62572]*) (*NotebookOutlinePosition[ 2754799, 62606]*) (* CellTagsIndexPosition[ 2754755, 62602]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["1.2 Folgen", "Section"], Cell[TextData[{ "Materialien zur Vorlesung ", StyleBox["Elementare Analysis", FontWeight->"Bold"], ", Wintersemester 2003 / 4" }], "SmallText"], Cell[TextData[{ "Bei der Berechnung von \[Pi] betrachtete ", ButtonBox["ARCHIMEDES", ButtonData:>{ URL[ "http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Archimedes.\ html"], None}, ButtonStyle->"Hyperlink"], " regelm\[ADoubleDot]\[SZ]ige ", StyleBox["n-", FontSlant->"Italic"], "Ecke mit 6, 12, 24, 48, 96 Ecken, also mit ", Cell[BoxData[ \(TraditionalForm\`6\[CenterDot]2\^0\)]], ", ", Cell[BoxData[ \(TraditionalForm\`6\[CenterDot]2\^1\)]], ", ", Cell[BoxData[ \(TraditionalForm\`6\[CenterDot]2\^2\)]], ", ", Cell[BoxData[ \(TraditionalForm\`6\[CenterDot]2\^3\)]], ", ", Cell[BoxData[ \(TraditionalForm\`6\[CenterDot]2\^4\)]], " Ecken. Die Seitenl\[ADoubleDot]ngen bei den Schneeflockenkurven waren ", StyleBox["a", FontSlant->"Italic"], ", ", StyleBox["a", FontSlant->"Italic"], "/3, ", StyleBox["a", FontSlant->"Italic"], "/9, ... , d.h. ", Cell[BoxData[ \(TraditionalForm\`a\[CenterDot]3\^\(-0\)\)]], ", ", Cell[BoxData[ \(TraditionalForm\`a\[CenterDot]3\^\(-1\)\)]], ", ", Cell[BoxData[ \(TraditionalForm\`a\[CenterDot]3\^\(-2\)\)]], ", ", Cell[BoxData[ \(TraditionalForm\`a\[CenterDot]3\^\(-3\)\)]], ", ", Cell[BoxData[ \(TraditionalForm\`a\[CenterDot]3\^\(-4\)\)]], ", ... . In beiden F\[ADoubleDot]llen lassen sich die Werte allgemein so \ darstellen: ", StyleBox["c", FontSlant->"Italic"], " \[CenterDot] ", Cell[BoxData[ \(TraditionalForm\`q\^n\)]], " , wobei ", Cell[BoxData[ \(TraditionalForm\`c, q \[Element] \[DoubleStruckCapitalR]\)]], " und ", StyleBox["n", FontSlant->"Italic"], " \[Element] \[DoubleStruckCapitalN] , der Menge der \ nat\[UDoubleDot]rlichen Zahlen.\n\nWie sehen ", StyleBox["c", FontSlant->"Italic"], " und ", StyleBox["q ", FontSlant->"Italic"], "in den beiden Beispielen jeweils aus? Die obigen Beobachtungen und viele \ \[ADoubleDot]hnliche f\[UDoubleDot]hren zu der grundlegenden " }], "Text"], Cell[TextData[{ StyleBox["Definition 1.2.1:", FontFamily->"Arial", FontVariations->{"Underline"->True}], StyleBox[" \nF", FontFamily->"Arial"], StyleBox["OLGE", FontFamily->"Arial", FontSize->10], "\nEs sei ", StyleBox["a", FontSlant->"Italic"], " : \[DoubleStruckCapitalN] \[RightArrow] \[DoubleStruckCapitalR] eine \ Abbildung. Dann hei\[SZ]t ", StyleBox["a", FontSlant->"Italic"], " ", StyleBox["R", FontFamily->"Arial"], StyleBox["EELLE", FontFamily->"Arial", FontSize->10], StyleBox[" F", FontFamily->"Arial"], StyleBox["OLGE", FontFamily->"Arial", FontSize->10], ". ", StyleBox["a", FontSlant->"Italic"], "(", StyleBox["n", FontSlant->"Italic"], ") hei\[SZ]t das ", StyleBox["n", FontFamily->"Arial", FontSlant->"Italic"], StyleBox["-te F", FontFamily->"Arial"], StyleBox["OLGENGLIED", FontFamily->"Arial", FontSize->10], ". Daf\[UDoubleDot]r ist die k\[UDoubleDot]rzere Schreibweise ", Cell[BoxData[ \(TraditionalForm\`a\_n\)]], " gebr\[ADoubleDot]uchlich. Statt ", StyleBox["a", FontSlant->"Italic"], " : \[DoubleStruckCapitalN] \[RightArrow] \[DoubleStruckCapitalR] finden \ Sie in der Literatur u.a. folgende Schreibweisen:\n\t", Cell[BoxData[ \(TraditionalForm\`\[LeftAngleBracket]a\_n\[RightAngleBracket]\_\(n \ \[Element] \[DoubleStruckCapitalN]\)\)]], " , ", Cell[BoxData[ \(TraditionalForm\`\[LeftAngleBracket]a\_n\[RightAngleBracket]\)]], " , ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " , ( ", Cell[BoxData[ \(TraditionalForm\`\(\(a\_1\)\(,\)\(\ \)\(a\_2\)\(,\)\(\ \ \)\(a\_3\)\(,\)\(\ \)\(a\_4\)\(,\)\(\ \)\(...\)\(\ \)\)\)]], ") .\nManchmal wird auch von unendlichen Folgen gesprochen. Ebenso \ hei\[SZ]t es oft nur Folge statt reelle Folge." }], "Text"], Cell[TextData[{ StyleBox["Definition 1.2.2:", FontFamily->"Arial", FontVariations->{"Underline"->True}], StyleBox[" \nG", FontFamily->"Arial"], StyleBox["EOMETRISCHE", FontFamily->"Arial", FontSize->10], StyleBox[" F", FontFamily->"Arial"], StyleBox["OLGE", FontFamily->"Arial", FontSize->10], "\nEs seien ", Cell[BoxData[ \(TraditionalForm\`c, \ q\ \[Element] \ \[DoubleStruckCapitalR]\)]], " . Die Folge ", StyleBox["g", FontSlant->"Italic"], " mit ", Cell[BoxData[ \(TraditionalForm\`\(\(\ \)\(g\_n\)\)\)]], " := ", StyleBox["c", FontSlant->"Italic"], " \[CenterDot] ", Cell[BoxData[ \(TraditionalForm\`q\^n\)]], " hei\[SZ]t ", StyleBox["G", FontFamily->"Arial"], StyleBox["EOMETRISCHE", FontFamily->"Arial", FontSize->10], StyleBox[" F", FontFamily->"Arial"], StyleBox["OLGE", FontFamily->"Arial", FontSize->10], ".\n\nIst ", StyleBox["q", FontSlant->"Italic"], " = 0 , so ist die geometrische Folge (", StyleBox["c", FontSlant->"Italic"], " \[CenterDot] ", Cell[BoxData[ \(TraditionalForm\`q\^n\)]], ") konstant: (0, 0, 0, ...) .\nIst ", StyleBox["q", FontSlant->"Italic"], " = 1, so ist die geometrische Folge (", StyleBox["c", FontSlant->"Italic"], " \[CenterDot] ", Cell[BoxData[ \(TraditionalForm\`q\^n\)]], ") auch konstant: (", StyleBox["c", FontSlant->"Italic"], ", ", StyleBox["c", FontSlant->"Italic"], ", ", StyleBox["c", FontSlant->"Italic"], ", ...) .\nIst ", StyleBox["q", FontSlant->"Italic"], " = \[Dash]1 und ", StyleBox["c", FontSlant->"Italic"], " \[NotEqual] 0, so alterniert die geometrische Folge: (\[Dash]", StyleBox["c", FontSlant->"Italic"], ", +", StyleBox["c", FontSlant->"Italic"], ", \[Dash]", StyleBox["c", FontSlant->"Italic"], ", +", StyleBox["c", FontSlant->"Italic"], ", ...) .\nDas Verhalten f\[UDoubleDot]r ", StyleBox["c", FontSlant->"Italic"], " \[NotEqual] 0, und | ", StyleBox["q", FontSlant->"Italic"], " | < 1 bzw. | ", StyleBox["q", FontSlant->"Italic"], " | > 1 werden wir sp\[ADoubleDot]ter genauer untersuchen.\nVorl\ \[ADoubleDot]ufig sollen nur drei Grafiken einen ersten Eindruck von diesen \ Folgen vermitteln." }], "Text"], Cell[TextData[{ "In den folgenden Beispielen ist ", StyleBox["c", FontSlant->"Italic"], " = 1 .\n Zuerst ist ", StyleBox["q", FontSlant->"Italic"], " = 1.014 :" }], "Text"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform 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\>"], ImageRangeCache->{{{87.4375, 316.813}, {405.688, 264.375}} -> {-29.04, \ 2.17257, 0.20567, 0.00697254}}], Cell[TextData[{ "Eine andere, nicht sehr anschauliche Darstellungsart bieten Tabellen, etwa \ f\[UDoubleDot]r ", Cell[BoxData[ \(TraditionalForm\`c = 1\)]], " und ", Cell[BoxData[ \(TraditionalForm\`q = 0.5\)]], " : \n\n", Cell[BoxData[ StyleBox[GridBox[{ { StyleBox["n", FontSlant-> "Italic"], \(\(\ \ \ \ \ \ \ \)\(1\)\(\ \ \ \ \ \ \)\), \ \(\(\ \ \ \ \ \ \ \)\(2\)\(\ \ \ \ \ \ \ \)\), \(\(\ \ \ \ \ \)\(3\)\(\ \ \ \ \ \ \)\), "4", "5", "6"}, { SuperscriptBox[ StyleBox["q", FontSlant->"Italic"], StyleBox["n", FontSlant->"Italic"]], "0.5", "0.25", \(\(\ \ \)\(0.125\)\(\ \ \)\), \(\(\ \ \)\(0.0625\)\(\ \ \)\), \(\(\ \)\(0.03125\)\), \(\(\ \ \)\(0.015625\)\)} }, RowLines->True, ColumnLines->True], FontFamily->"Times New Roman"]]], "\n" }], "Text"], Cell["\<\ In Tests finden sich h\[ADoubleDot]ufig Fragen folgender Art: Finden Sie das \ n\[ADoubleDot]chste Glied der \"Folge\" \t\t1, 1, 2, 3, 5 ? Eine derartige Fragestellung ist zumindest mi\[SZ]verst\[ADoubleDot]ndlich! \ Gemeint ist n\[ADoubleDot]mlich: K\[ODoubleDot]nnen Sie ein Bildungsgesetz \ der \"Folge\" erkennen, und wenn ja, bestimmen Sie dazu das \ n\[ADoubleDot]chste Glied der \"Folge\". Bei der eben angegebenen \"Folge\" (also den f\[UDoubleDot]nf Zahlen) lassen \ sich aber mindestens zwei v\[ODoubleDot]llig unterschiedliche Bildungsgesetze \ angeben: 1. Die \"Folge\" beginnt mit zwei Einsen und dann folgen die Primzahlen. \ Danach w\[ADoubleDot]re das n\[ADoubleDot]chste \"Folgenglied\" 7 . 2. Die \"Folge\" beginnt mit zwei Einsen und jedes folgende Glied ist die \ Summe der beiden vorhergehenden. Also ist das n\[ADoubleDot]chste \ \"Folgenglied\" 8 . Also: Vorsicht bei derartigen Aufgaben !!!\ \>", "Text"], Cell[TextData[{ "Folgen sind ", StyleBox["unendliche", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " Mengen! Meistens k\[ODoubleDot]nnen nur ", StyleBox["endlich viele", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " Elemente einer unendlichen Menge dargestellt werden. Trotzdem soll es \ versucht werden.\n\nBeispiele f\[UDoubleDot]r Folgen:\n\t\t\t( ", Cell[BoxData[ \(TraditionalForm\`\(\(a\_n\)\(\ \)\)\)]], ") := ", Cell[BoxData[ \(TraditionalForm\`\((\[NegativeThinSpace]\ 1\/n\ \[NegativeThinSpace])\ \)\)]], Cell[BoxData[ \(TraditionalForm\`\(\(\[NegativeThinSpace]\[NegativeThinSpace]\)\()\)\)\ \)]] }], "Text"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.0190476 0.0515028 0.515028 [ [.21429 .039 -8 -15.6875 ] [.21429 .039 8 0 ] [.40476 .039 -8 -15.6875 ] [.40476 .039 8 0 ] [.59524 .039 -8 -15.6875 ] [.59524 .039 8 0 ] [.78571 .039 -8 -15.6875 ] [.78571 .039 8 0 ] [.97619 .039 -8 -15.6875 ] [.97619 .039 8 0 ] [.01131 .05202 -19 -7.84375 ] 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Das muss aber nicht \ so sein. Dazu erinnern Sie sich an die Definition des Teilers einer nat\ \[UDoubleDot]rlichen Zahl. 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.12976 Mdot .1581 .01575 Mdot .15833 .17137 Mdot .15857 .45354 Mdot .15881 .60284 Mdot .15905 .48199 Mdot .15929 .20212 Mdot .15952 .02052 Mdot .15976 .10417 Mdot .16 .37615 Mdot .16024 .58641 Mdot .16048 .54163 Mdot .16071 .28299 Mdot .16095 .04828 Mdot .16119 .05329 Mdot .16143 .29341 Mdot .16167 .54789 Mdot .1619 .58274 Mdot .16214 .36594 Mdot .16238 .0968 Mdot .16262 .02277 Mdot .16286 .21192 Mdot .1631 .49033 Mdot .16333 .60205 Mdot .16357 .44435 Mdot .16381 .16223 Mdot .16405 .01506 Mdot .16429 .13816 Mdot .16452 .41834 Mdot .16476 .59801 Mdot .165 .51199 Mdot .16524 .23935 Mdot .16548 .03077 Mdot .16571 .078 Mdot .16595 .33764 Mdot .16619 .57095 Mdot .16643 .56345 Mdot .16667 .32202 Mdot .1669 .06864 Mdot .16714 .03626 Mdot .16738 .25465 Mdot .16762 .52303 Mdot .16786 .59465 Mdot .1681 .40366 Mdot .16833 .12565 Mdot .16857 .01624 Mdot .16881 .176 Mdot .16905 .45806 Mdot .16929 .60309 Mdot .16952 .47775 Mdot .16976 .19728 Mdot .17 .01954 Mdot .17024 .10794 Mdot .17048 .38121 Mdot .17071 .58811 Mdot .17095 .53841 Mdot .17119 .27781 Mdot .17143 .0459 Mdot .17167 .0559 Mdot .1719 .29862 Mdot .17214 .55089 Mdot .17238 .58079 Mdot .17262 .36082 Mdot .17286 .09322 Mdot .1731 .02403 Mdot .17333 .21685 Mdot .17357 .49441 Mdot .17381 .60152 Mdot .17405 .43971 Mdot .17429 .15774 Mdot .17452 .01485 Mdot .17476 .14242 Mdot .175 .42316 Mdot .17524 .59895 Mdot .17548 .50818 Mdot .17571 .2343 Mdot .17595 .02911 Mdot .17619 .08127 Mdot .17643 .34282 Mdot .17667 .57329 Mdot .1769 .56079 Mdot .17714 .31681 Mdot .17738 .06567 Mdot .17762 .03826 Mdot .17786 .25978 Mdot .1781 .52657 Mdot .17833 .59335 Mdot .17857 .39871 Mdot .17881 .12161 Mdot .17905 .01681 Mdot .17929 .18067 Mdot .17952 .46253 Mdot .17976 .60325 Mdot .18 .47346 Mdot .18024 .19248 Mdot .18048 .01865 Mdot .18071 .11178 Mdot .18095 .38625 Mdot .18119 .58972 Mdot .18143 .53511 Mdot .18167 .27263 Mdot .1819 .04361 Mdot .18214 .0586 Mdot .18238 .30382 Mdot .18262 .55382 Mdot .18286 .57875 Mdot .1831 .35568 Mdot .18333 .08972 Mdot .18357 .02537 Mdot .18381 .22181 Mdot .18405 .49843 Mdot .18429 .6009 Mdot .18452 .43502 Mdot .18476 .15329 Mdot .185 .01474 Mdot .18524 .14674 Mdot .18548 .42794 Mdot .18571 .5998 Mdot .18595 .50431 Mdot .18619 .22927 Mdot .18643 .02755 Mdot .18667 .0846 Mdot .1869 .34799 Mdot .18714 .57554 Mdot .18738 .55805 Mdot .18762 .3116 Mdot .18786 .06278 Mdot .1881 .04034 Mdot .18833 .26493 Mdot .18857 .53005 Mdot .18881 .59196 Mdot .18905 .39373 Mdot .18929 .11762 Mdot .18952 .01748 Mdot .18976 .18538 Mdot .19 .46695 Mdot .19024 .60332 Mdot .19048 .46911 Mdot .19071 .18771 Mdot .19095 .01784 Mdot .19119 .11568 Mdot .19143 .39127 Mdot .19167 .59124 Mdot .1919 .53174 Mdot .19214 .26747 Mdot .19238 .0414 Mdot .19262 .06138 Mdot .19286 .30903 Mdot .1931 .55668 Mdot .19333 .57662 Mdot .19357 .35053 Mdot .19381 .08628 Mdot .19405 .02681 Mdot .19429 .2268 Mdot .19452 .50238 Mdot .19476 .60019 Mdot .195 .43029 Mdot .19524 .14889 Mdot .19548 .01472 Mdot .19571 .15112 Mdot .19595 .43269 Mdot .19619 .60056 Mdot .19643 .50039 Mdot .19667 .22427 Mdot .1969 .02607 Mdot .19714 .08801 Mdot .19738 .35314 Mdot .19762 .57771 Mdot .19786 .55524 Mdot .1981 .30639 Mdot .19833 .05996 Mdot .19857 .04251 Mdot .19881 .27008 Mdot .19905 .53345 Mdot .19929 .59048 Mdot .19952 .38873 Mdot .19976 .11369 Mdot .2 .01824 Mdot .20024 .19012 Mdot .20048 .47132 Mdot .20071 .6033 Mdot .20095 .46471 Mdot .20119 .18298 Mdot .20143 .01713 Mdot .20167 .11963 Mdot .2019 .39626 Mdot .20214 .59267 Mdot .20238 .5283 Mdot .20262 .26232 Mdot .20286 .03927 Mdot .2031 .06423 Mdot .20333 .31424 Mdot .20357 .55945 Mdot .20381 .57441 Mdot .20405 .34537 Mdot .20429 .0829 Mdot .20452 .02833 Mdot .20476 .23182 Mdot .205 .50628 Mdot .20524 .59938 Mdot .20548 .42552 Mdot .20571 .14455 Mdot .20595 .01479 Mdot .20619 .15554 Mdot .20643 .4374 Mdot .20667 .60123 Mdot .2069 .4964 Mdot .20714 .21929 Mdot .20738 .02468 Mdot .20762 .09148 Mdot .20786 .35829 Mdot .2081 .57979 Mdot .20833 .55235 Mdot .20857 .30119 Mdot .20881 .05722 Mdot .20905 .04476 Mdot .20929 .27525 Mdot .20952 .53679 Mdot .20976 .58891 Mdot .21 .3837 Mdot .21024 .10983 Mdot .21048 .01909 Mdot .21071 .19491 Mdot .21095 .47564 Mdot .21119 .60318 Mdot .21143 .46027 Mdot .21167 .1783 Mdot .2119 .01651 Mdot .21214 .12365 Mdot .21238 .40122 Mdot .21262 .59402 Mdot .21286 .52479 Mdot .2131 .25718 Mdot .21333 .03723 Mdot .21357 .06716 Mdot .21381 .31945 Mdot .21405 .56215 Mdot .21429 .57212 Mdot .21452 .34019 Mdot .21476 .07961 Mdot .215 .02994 Mdot .21524 .23686 Mdot .21548 .51012 Mdot .21571 .59849 Mdot .21595 .42072 Mdot .21619 .14025 Mdot .21643 .01495 Mdot .21667 .16001 Mdot .2169 .44207 Mdot .21714 .6018 Mdot .21738 .49235 Mdot .21762 .21435 Mdot .21786 .02338 Mdot .2181 .09503 Mdot .21833 .36342 Mdot .21857 .58179 Mdot .21881 .54938 Mdot .21905 .29598 Mdot .21929 .05457 Mdot .21952 .0471 Mdot .21976 .28043 Mdot .22 .54005 Mdot .22024 .58726 Mdot .22048 .37865 Mdot .22071 .10602 Mdot .22095 .02003 Mdot .22119 .19973 Mdot .22143 .47991 Mdot .22167 .60297 Mdot .2219 .45578 Mdot .22214 .17365 Mdot .22238 .01598 Mdot .22262 .12773 Mdot .22286 .40615 Mdot .2231 .59527 Mdot .22333 .52121 Mdot .22357 .25206 Mdot .22381 .03528 Mdot .22405 .07017 Mdot .22429 .32466 Mdot .22452 .56477 Mdot .22476 .56974 Mdot .225 .33501 Mdot .22524 .07638 Mdot .22548 .03164 Mdot .22571 .24192 Mdot .22595 .51389 Mdot .22619 .5975 Mdot .22643 .41588 Mdot .22667 .13601 Mdot .2269 .0152 Mdot .22714 .16452 Mdot .22738 .44669 Mdot .22762 .60228 Mdot .22786 .48825 Mdot .2281 .20943 Mdot .22833 .02217 Mdot .22857 .09864 Mdot .22881 .36853 Mdot .22905 .5837 Mdot .22929 .54633 Mdot .22952 .29078 Mdot .22976 .05199 Mdot .23 .04951 Mdot .23024 .28562 Mdot .23048 .54324 Mdot .23071 .58552 Mdot .23095 .37358 Mdot .23119 .10228 Mdot .23143 .02106 Mdot .23167 .20458 Mdot .2319 .48412 Mdot .23214 .60267 Mdot .23238 .45124 Mdot .23262 .16904 Mdot .23286 .01554 Mdot .2331 .13186 Mdot .23333 .41105 Mdot .23357 .59644 Mdot .23381 .51757 Mdot .23405 .24696 Mdot .23429 .03341 Mdot .23452 .07325 Mdot .23476 .32986 Mdot .235 .5673 Mdot .23524 .56728 Mdot .23548 .32981 Mdot .23571 .07322 Mdot .23595 .03342 Mdot .23619 .247 Mdot .23643 .5176 Mdot .23667 .59643 Mdot .2369 .41101 Mdot .23714 .13182 Mdot .23738 .01555 Mdot .23762 .16908 Mdot .23786 .45128 Mdot .2381 .60267 Mdot .23833 .48409 Mdot .23857 .20454 Mdot .23881 .02105 Mdot .23905 .10231 Mdot .23929 .37362 Mdot .23952 .58553 Mdot .23976 .54322 Mdot .24 .28558 Mdot .24024 .04949 Mdot .24048 .05201 Mdot .24071 .29082 Mdot .24095 .54636 Mdot .24119 .58369 Mdot .24143 .36848 Mdot .24167 .09861 Mdot .2419 .02218 Mdot .24214 .20947 Mdot .24238 .48828 Mdot .24262 .60228 Mdot .24286 .44665 Mdot .2431 .16448 Mdot .24333 .0152 Mdot .24357 .13605 Mdot .24381 .41592 Mdot .24405 .59751 Mdot .24429 .51386 Mdot .24452 .24187 Mdot .24476 .03162 Mdot .245 .07641 Mdot .24524 .33505 Mdot .24548 .56976 Mdot .24571 .56474 Mdot .24595 .32461 Mdot .24619 .07014 Mdot .24643 .03529 Mdot .24667 .2521 Mdot .2469 .52124 Mdot .24714 .59526 Mdot .24738 .40611 Mdot .24762 .12769 Mdot .24786 .01598 Mdot .2481 .17369 Mdot .24833 .45581 Mdot .24857 .60297 Mdot .24881 .47987 Mdot .24905 .19969 Mdot .24929 .02002 Mdot .24952 .10606 Mdot .24976 .37869 Mdot .25 .58727 Mdot .25024 .54002 Mdot .25048 .28039 Mdot .25071 .04708 Mdot .25095 .05459 Mdot .25119 .29602 Mdot .25143 .5494 Mdot .25167 .58177 Mdot .2519 .36337 Mdot .25214 .095 Mdot .25238 .02339 Mdot .25262 .21439 Mdot .25286 .49239 Mdot .2531 .6018 Mdot .25333 .44203 Mdot .25357 .15997 Mdot .25381 .01495 Mdot .25405 .14029 Mdot .25429 .42076 Mdot .25452 .5985 Mdot .25476 .51008 Mdot .255 .23681 Mdot .25524 .02992 Mdot .25548 .07963 Mdot .25571 .34024 Mdot .25595 .57214 Mdot .25619 .56213 Mdot .25643 .31941 Mdot .25667 .06714 Mdot .2569 .03725 Mdot .25714 .25722 Mdot .25738 .52482 Mdot .25762 .594 Mdot .25786 .40118 Mdot .2581 .12362 Mdot .25833 .01651 Mdot .25857 .17834 Mdot .25881 .46031 Mdot .25905 .60318 Mdot .25929 .4756 Mdot .25952 .19487 Mdot .25976 .01908 Mdot .26 .10986 Mdot .26024 .38374 Mdot .26048 .58892 Mdot .26071 .53676 Mdot .26095 .27521 Mdot .26119 .04474 Mdot .26143 .05725 Mdot .26167 .30123 Mdot .2619 .55237 Mdot .26214 .57977 Mdot .26238 .35824 Mdot .26262 .09145 Mdot .26286 .02469 Mdot .2631 .21934 Mdot .26333 .49643 Mdot .26357 .60122 Mdot .26381 .43736 Mdot .26405 .1555 Mdot .26429 .01478 Mdot .26452 .14459 Mdot .26476 .42556 Mdot .265 .59939 Mdot .26524 .50625 Mdot .26548 .23177 Mdot .26571 .02832 Mdot .26595 .08293 Mdot .26619 .34541 Mdot .26643 .57443 Mdot .26667 .55943 Mdot .2669 .3142 Mdot .26714 .06421 Mdot .26738 .03929 Mdot .26762 .26236 Mdot .26786 .52832 Mdot .2681 .59266 Mdot .26833 .39621 Mdot .26857 .1196 Mdot .26881 .01714 Mdot .26905 .18303 Mdot .26929 .46475 Mdot .26952 .6033 Mdot .26976 .47128 Mdot .27 .19008 Mdot .27024 .01823 Mdot .27048 .11373 Mdot .27071 .38877 Mdot .27095 .59049 Mdot .27119 .53342 Mdot .27143 .27004 Mdot .27167 .04249 Mdot .2719 .05998 Mdot .27214 .30644 Mdot .27238 .55526 Mdot .27262 .57769 Mdot .27286 .3531 Mdot .2731 .08798 Mdot .27333 .02608 Mdot .27357 .22431 Mdot .27381 .50042 Mdot .27405 .60055 Mdot .27429 .43265 Mdot .27452 .15108 Mdot .27476 .01472 Mdot .275 .14893 Mdot .27524 .43033 Mdot .27548 .60019 Mdot .27571 .50235 Mdot .27595 .22676 Mdot .27619 .02679 Mdot .27643 .0863 Mdot .27667 .35058 Mdot .2769 .57664 Mdot .27714 .55665 Mdot .27738 .30899 Mdot .27762 .06135 Mdot .27786 .04142 Mdot .2781 .26751 Mdot .27833 .53176 Mdot .27857 .59123 Mdot .27881 .39122 Mdot .27905 .11564 Mdot .27929 .01785 Mdot .27952 .18775 Mdot .27976 .46915 Mdot .28 .60332 Mdot .28024 .46691 Mdot .28048 .18534 Mdot .28071 .01747 Mdot .28095 .11765 Mdot .28119 .39377 Mdot .28143 .59197 Mdot .28167 .53002 Mdot .2819 .26488 Mdot .28214 .04032 Mdot .28238 .0628 Mdot .28262 .31165 Mdot .28286 .55808 Mdot .2831 .57552 Mdot .28333 .34794 Mdot .28357 .08458 Mdot .28381 .02756 Mdot .28405 .22931 Mdot .28429 .50435 Mdot .28452 .59979 Mdot .28476 .4279 Mdot .285 .14671 Mdot .28524 .01474 Mdot .28548 .15333 Mdot .28571 .43506 Mdot .28595 .60091 Mdot .28619 .49839 Mdot .28643 .22177 Mdot .28667 .02536 Mdot .2869 .08974 Mdot .28714 .35573 Mdot .28738 .57876 Mdot .28762 .5538 Mdot .28786 .30378 Mdot .2881 .05858 Mdot .28833 .04363 Mdot .28857 .27268 Mdot .28881 .53513 Mdot .28905 .5897 Mdot .28929 .38621 Mdot .28952 .11175 Mdot .28976 .01865 Mdot .29 .19252 Mdot .29024 .47349 Mdot .29048 .60325 Mdot .29071 .46249 Mdot .29095 .18063 Mdot .29119 .01681 Mdot .29143 .12164 Mdot .29167 .39875 Mdot .2919 .59336 Mdot .29214 .52654 Mdot .29238 .25974 Mdot .29262 .03824 Mdot .29286 .06569 Mdot .2931 .31686 Mdot .29333 .56081 Mdot .29357 .57327 Mdot .29381 .34277 Mdot .29405 .08124 Mdot .29429 .02913 Mdot .29452 .23434 Mdot .29476 .50821 Mdot .295 .59895 Mdot .29524 .42312 Mdot .29548 .14239 Mdot .29571 .01485 Mdot .29595 .15777 Mdot .29619 .43975 Mdot .29643 .60153 Mdot .29667 .49438 Mdot .2969 .21681 Mdot .29714 .02402 Mdot .29738 .09325 Mdot .29762 .36086 Mdot .29786 .58081 Mdot .2981 .55087 Mdot .29833 .29857 Mdot .29857 .05588 Mdot .29881 .04592 Mdot .29905 .27785 Mdot .29929 .53843 Mdot .29952 .58809 Mdot .29976 .38117 Mdot .3 .10791 Mdot .30024 .01955 Mdot .30048 .19732 Mdot .30071 .47779 Mdot .30095 .60309 Mdot .30119 .45802 Mdot .30143 .17596 Mdot .30167 .01623 Mdot .3019 .12569 Mdot .30214 .4037 Mdot .30238 .59466 Mdot .30262 .523 Mdot .30286 .25461 Mdot .3031 .03624 Mdot .30333 .06866 Mdot .30357 .32206 Mdot .30381 .56347 Mdot .30405 .57093 Mdot .30429 .33759 Mdot .30452 .07798 Mdot .30476 .03078 Mdot .305 .23939 Mdot .30524 .51202 Mdot .30548 .598 Mdot .30571 .4183 Mdot .30595 .13812 Mdot .30619 .01506 Mdot .30643 .16227 Mdot .30667 .44439 Mdot .3069 .60205 Mdot .30714 .4903 Mdot .30738 .21187 Mdot .30762 .02276 Mdot .30786 .09683 Mdot .3081 .36598 Mdot .30833 .58276 Mdot .30857 .54786 Mdot .30881 .29337 Mdot .30905 .05326 Mdot .30929 .0483 Mdot .30952 .28304 Mdot .30976 .54166 Mdot .31 .58639 Mdot .31024 .37611 Mdot .31048 .10414 Mdot .31071 .02053 Mdot .31095 .20216 Mdot .31119 .48203 Mdot .31143 .60283 Mdot .31167 .4535 Mdot .3119 .17133 Mdot .31214 .01575 Mdot .31238 .12979 Mdot .31262 .40862 Mdot .31286 .59587 Mdot .3131 .51939 Mdot .31333 .2495 Mdot .31357 .03433 Mdot .31381 .07171 Mdot .31405 .32727 Mdot .31429 .56605 Mdot .31452 .56852 Mdot .31476 .3324 Mdot .315 .07479 Mdot .31524 .03252 Mdot .31548 .24447 Mdot .31571 .51576 Mdot .31595 .59697 Mdot .31619 .41344 Mdot .31643 .1339 Mdot .31667 .01536 Mdot .3169 .16681 Mdot .31714 .449 Mdot .31738 .60249 Mdot .31762 .48617 Mdot .31786 .20697 Mdot .3181 .0216 Mdot .31833 .10047 Mdot .31857 .37109 Mdot .31881 .58463 Mdot .31905 .54478 Mdot .31929 .28817 Mdot .31952 .05073 Mdot .31976 .05076 Mdot .32 .28823 Mdot .32024 .54482 Mdot .32048 .58461 Mdot .32071 .37102 Mdot .32095 .10043 Mdot .32119 .02161 Mdot .32143 .20703 Mdot .32167 .48622 Mdot .3219 .60249 Mdot .32214 .44894 Mdot .32238 .16675 Mdot .32262 .01536 Mdot .32286 .13395 Mdot .3231 .4135 Mdot .32333 .59699 Mdot .32357 .51571 Mdot .32381 .2444 Mdot .32405 .0325 Mdot .32429 .07482 Mdot .32452 .33246 Mdot .32476 .56855 Mdot .325 .56602 Mdot .32524 .32721 Mdot .32548 .07167 Mdot .32571 .03435 Mdot .32595 .24956 Mdot .32619 .51943 Mdot .32643 .59585 Mdot .32667 .40856 Mdot .3269 .12974 Mdot .32714 .01575 Mdot .32738 .17139 Mdot .32762 .45356 Mdot .32786 .60284 Mdot .3281 .48198 Mdot .32833 .2021 Mdot .32857 .02052 Mdot .32881 .10418 Mdot .32905 .37617 Mdot .32929 .58642 Mdot .32952 .54162 Mdot .32976 .28297 Mdot .33 .04827 Mdot .33024 .05329 Mdot .33048 .29343 Mdot .33071 .5479 Mdot .33095 .58274 Mdot .33119 .36592 Mdot .33143 .09679 Mdot .33167 .02278 Mdot .3319 .21193 Mdot .33214 .49035 Mdot .33238 .60205 Mdot .33262 .44434 Mdot .33286 .16221 Mdot .3331 .01506 Mdot .33333 .13817 Mdot .33357 .41836 Mdot .33381 .59802 Mdot .33405 .51197 Mdot .33429 .23933 Mdot .33452 .03076 Mdot .33476 .07802 Mdot .335 .33765 Mdot .33524 .57096 Mdot .33548 .56344 Mdot .33571 .322 Mdot .33595 .06863 Mdot .33619 .03626 Mdot .33643 .25467 Mdot .33667 .52304 Mdot .3369 .59464 Mdot .33714 .40364 Mdot .33738 .12564 Mdot .33762 .01624 Mdot .33786 .17602 Mdot .3381 .45807 Mdot .33833 .60309 Mdot .33857 .47774 Mdot .33881 .19726 Mdot .33905 .01954 Mdot .33929 .10796 Mdot .33952 .38123 Mdot .33976 .58811 Mdot .34 .5384 Mdot .34024 .27779 Mdot .34048 .04589 Mdot .34071 .05591 Mdot .34095 .29863 Mdot .34119 .5509 Mdot .34143 .58078 Mdot .34167 .3608 Mdot .3419 .09321 Mdot .34214 .02403 Mdot .34238 .21687 Mdot .34262 .49442 Mdot .34286 .60152 Mdot .3431 .43969 Mdot .34333 .15772 Mdot .34357 .01485 Mdot .34381 .14244 Mdot .34405 .42318 Mdot .34429 .59896 Mdot .34452 .50817 Mdot .34476 .23428 Mdot .345 .02911 Mdot .34524 .08128 Mdot .34548 .34283 Mdot .34571 .5733 Mdot .34595 .56078 Mdot .34619 .3168 Mdot .34643 .06566 Mdot .34667 .03826 Mdot .3469 .2598 Mdot .34714 .52659 Mdot .34738 .59334 Mdot .34762 .39869 Mdot .34786 .12159 Mdot .3481 .01681 Mdot .34833 .18068 Mdot .34857 .46254 Mdot .34881 .60325 Mdot .34905 .47344 Mdot .34929 .19246 Mdot .34952 .01864 Mdot .34976 .11179 Mdot .35 .38627 Mdot .35024 .58972 Mdot .35048 .5351 Mdot .35071 .27261 Mdot .35095 .0436 Mdot .35119 .05861 Mdot .35143 .30384 Mdot .35167 .55383 Mdot .3519 .57874 Mdot .35214 .35567 Mdot .35238 .0897 Mdot .35262 .02538 Mdot .35286 .22183 Mdot .3531 .49844 Mdot .35333 .6009 Mdot .35357 .435 Mdot .35381 .15328 Mdot .35405 .01474 Mdot .35429 .14676 Mdot .35452 .42796 Mdot .35476 .5998 Mdot .355 .5043 Mdot .35524 .22925 Mdot .35548 .02754 Mdot .35571 .08462 Mdot .35595 .348 Mdot .35619 .57555 Mdot .35643 .55804 Mdot .35667 .31159 Mdot .3569 .06277 Mdot .35714 .04035 Mdot .35738 .26494 Mdot .35762 .53006 Mdot .35786 .59195 Mdot .3581 .39371 Mdot .35833 .11761 Mdot .35857 .01748 Mdot .35881 .18539 Mdot .35905 .46696 Mdot .35929 .60332 Mdot .35952 .4691 Mdot .35976 .1877 Mdot .36 .01784 Mdot .36024 .11569 Mdot .36048 .39128 Mdot .36071 .59124 Mdot .36095 .53172 Mdot .36119 .26745 Mdot .36143 .04139 Mdot .36167 .06139 Mdot .3619 .30905 Mdot .36214 .55668 Mdot .36238 .57661 Mdot .36262 .35051 Mdot .36286 .08626 Mdot .3631 .02681 Mdot .36333 .22682 Mdot .36357 .5024 Mdot .36381 .60018 Mdot .36405 .43027 Mdot .36429 .14888 Mdot .36452 .01472 Mdot .36476 .15113 Mdot .365 .43271 Mdot .36524 .60056 Mdot .36548 .50037 Mdot .36571 .22425 Mdot .36595 .02606 Mdot .36619 .08802 Mdot .36643 .35316 Mdot .36667 .57772 Mdot .3669 .55523 Mdot .36714 .30638 Mdot .36738 .05995 Mdot .36762 .04252 Mdot .36786 .2701 Mdot .3681 .53346 Mdot .36833 .59047 Mdot .36857 .38871 Mdot .36881 .11368 Mdot .36905 .01824 Mdot .36929 .19014 Mdot .36952 .47133 Mdot .36976 .60329 Mdot .37 .4647 Mdot .37024 .18297 Mdot .37048 .01713 Mdot .37071 .11965 Mdot .37095 .39627 Mdot .37119 .59268 Mdot .37143 .52828 Mdot .37167 .2623 Mdot .3719 .03927 Mdot .37214 .06424 Mdot .37238 .31426 Mdot .37262 .55946 Mdot .37286 .5744 Mdot .3731 .34535 Mdot .37333 .08289 Mdot .37357 .02833 Mdot .37381 .23183 Mdot .37405 .50629 Mdot .37429 .59938 Mdot .37452 .42551 Mdot .37476 .14453 Mdot .375 .01479 Mdot .37524 .15555 Mdot .37548 .43741 Mdot .37571 .60123 Mdot .37595 .49638 Mdot .37619 .21928 Mdot .37643 .02468 Mdot .37667 .0915 Mdot .3769 .35831 Mdot .37714 .5798 Mdot .37738 .55234 Mdot .37762 .30117 Mdot .37786 .05722 Mdot .3781 .04477 Mdot .37833 .27527 Mdot .37857 .5368 Mdot .37881 .58891 Mdot .37905 .38368 Mdot .37929 .10981 Mdot .37952 .01909 Mdot .37976 .19492 Mdot .38 .47565 Mdot .38024 .60318 Mdot .38048 .46025 Mdot .38071 .17828 Mdot .38095 .01651 Mdot .38119 .12367 Mdot .38143 .40124 Mdot .38167 .59402 Mdot .3819 .52477 Mdot .38214 .25716 Mdot .38238 .03723 Mdot .38262 .06717 Mdot .38286 .31947 Mdot .3831 .56216 Mdot .38333 .57211 Mdot .38357 .34017 Mdot .38381 .07959 Mdot .38405 .02994 Mdot .38429 .23687 Mdot .38452 .51013 Mdot .38476 .59848 Mdot .385 .4207 Mdot .38524 .14024 Mdot .38548 .01495 Mdot .38571 .16002 Mdot .38595 .44208 Mdot .38619 .6018 Mdot .38643 .49234 Mdot .38667 .21433 Mdot .3869 .02338 Mdot .38714 .09504 Mdot .38738 .36343 Mdot .38762 .5818 Mdot .38786 .54937 Mdot .3881 .29596 Mdot .38833 .05456 Mdot .38857 .0471 Mdot .38881 .28045 Mdot .38905 .54006 Mdot .38929 .58725 Mdot .38952 .37863 Mdot .38976 .10601 Mdot .39 .02003 Mdot .39024 .19974 Mdot .39048 .47992 Mdot .39071 .60297 Mdot .39095 .45576 Mdot .39119 .17363 Mdot .39143 .01598 Mdot .39167 .12774 Mdot .3919 .40617 Mdot .39214 .59527 Mdot .39238 .5212 Mdot .39262 .25204 Mdot .39286 .03527 Mdot .3931 .07018 Mdot .39333 .32468 Mdot .39357 .56478 Mdot .39381 .56973 Mdot .39405 .33499 Mdot .39429 .07637 Mdot .39452 .03164 Mdot .39476 .24193 Mdot .395 .5139 Mdot .39524 .5975 Mdot .39548 .41587 Mdot .39571 .136 Mdot .39595 .0152 Mdot .39619 .16454 Mdot .39643 .44671 Mdot .39667 .60229 Mdot .3969 .48823 Mdot .39714 .20941 Mdot .39738 .02217 Mdot .39762 .09865 Mdot .39786 .36855 Mdot .3981 .58371 Mdot .39833 .54632 Mdot .39857 .29076 Mdot .39881 .05198 Mdot .39905 .04952 Mdot .39929 .28564 Mdot .39952 .54325 Mdot .39976 .58551 Mdot .4 .37356 Mdot .40024 .10227 Mdot .40048 .02106 Mdot .40071 .2046 Mdot .40095 .48414 Mdot .40119 .60267 Mdot .40143 .45122 Mdot .40167 .16903 Mdot .4019 .01554 Mdot .40214 .13187 Mdot .40238 .41107 Mdot .40262 .59644 Mdot .40286 .51755 Mdot .4031 .24694 Mdot .40333 .0334 Mdot .40357 .07326 Mdot .40381 .32988 Mdot .40405 .56731 Mdot .40429 .56727 Mdot .40452 .3298 Mdot .40476 .07321 Mdot .405 .03343 Mdot .40524 .24702 Mdot .40548 .51761 Mdot .40571 .59642 Mdot .40595 .411 Mdot .40619 .13181 Mdot .40643 .01555 Mdot .40667 .1691 Mdot .4069 .45129 Mdot .40714 .60268 Mdot .40738 .48407 Mdot .40762 .20452 Mdot .40786 .02105 Mdot .4081 .10233 Mdot .40833 .37364 Mdot .40857 .58554 Mdot .40881 .5432 Mdot .40905 .28556 Mdot .40929 .04948 Mdot .40952 .05202 Mdot .40976 .29084 Mdot .41 .54637 Mdot .41024 .58368 Mdot .41048 .36847 Mdot .41071 .09859 Mdot .41095 .02218 Mdot .41119 .20949 Mdot .41143 .4883 Mdot .41167 .60228 Mdot .4119 .44664 Mdot .41214 .16447 Mdot .41238 .0152 Mdot .41262 .13606 Mdot .41286 .41594 Mdot .4131 .59751 Mdot .41333 .51384 Mdot .41357 .24186 Mdot .41381 .03162 Mdot .41405 .07642 Mdot .41429 .33507 Mdot .41452 .56977 Mdot .41476 .56474 Mdot .415 .3246 Mdot .41524 .07013 Mdot .41548 .0353 Mdot .41571 .25212 Mdot .41595 .52125 Mdot .41619 .59526 Mdot .41643 .40609 Mdot .41667 .12768 Mdot .4169 .01599 Mdot .41714 .1737 Mdot .41738 .45583 Mdot .41762 .60297 Mdot .41786 .47986 Mdot .4181 .19967 Mdot .41833 .02002 Mdot .41857 .10607 Mdot .41881 .37871 Mdot .41905 .58728 Mdot .41929 .54001 Mdot .41952 .28037 Mdot .41976 .04707 Mdot .42 .0546 Mdot .42024 .29604 Mdot .42048 .54941 Mdot .42071 .58177 Mdot .42095 .36336 Mdot .42119 .09499 Mdot .42143 .02339 Mdot .42167 .2144 Mdot .4219 .4924 Mdot .42214 .60179 Mdot .42238 .44201 Mdot .42262 .15995 Mdot .42286 .01494 Mdot .4231 .1403 Mdot .42333 .42078 Mdot .42357 .5985 Mdot .42381 .51007 Mdot .42405 .2368 Mdot .42429 .02992 Mdot .42452 .07964 Mdot .42476 .34025 Mdot .425 .57214 Mdot .42524 .56212 Mdot .42548 .31939 Mdot .42571 .06713 Mdot .42595 .03726 Mdot .42619 .25724 Mdot .42643 .52483 Mdot .42667 .594 Mdot .4269 .40116 Mdot .42714 .1236 Mdot .42738 .01652 Mdot .42762 .17835 Mdot .42786 .46032 Mdot .4281 .60318 Mdot .42833 .47559 Mdot .42857 .19485 Mdot .42881 .01908 Mdot .42905 .10987 Mdot .42929 .38376 Mdot .42952 .58893 Mdot .42976 .53675 Mdot .43 .27519 Mdot .43024 .04473 Mdot .43048 .05726 Mdot .43071 .30125 Mdot .43095 .55238 Mdot .43119 .57977 Mdot .43143 .35823 Mdot .43167 .09144 Mdot .4319 .0247 Mdot .43214 .21935 Mdot .43238 .49645 Mdot .43262 .60122 Mdot .43286 .43734 Mdot .4331 .15548 Mdot .43333 .01478 Mdot .43357 .1446 Mdot .43381 .42558 Mdot .43405 .59939 Mdot .43429 .50624 Mdot .43452 .23176 Mdot .43476 .02831 Mdot .435 .08294 Mdot .43524 .34543 Mdot .43548 .57444 Mdot .43571 .55942 Mdot .43595 .31418 Mdot .43619 .0642 Mdot .43643 .0393 Mdot .43667 .26238 Mdot .4369 .52834 Mdot .43714 .59265 Mdot .43738 .3962 Mdot .43762 .11959 Mdot .43786 .01714 Mdot .4381 .18304 Mdot .43833 .46477 Mdot .43857 .6033 Mdot .43881 .47127 Mdot .43905 .19007 Mdot .43929 .01823 Mdot .43952 .11374 Mdot .43976 .38879 Mdot .44 .5905 Mdot .44024 .53341 Mdot .44048 .27002 Mdot .44071 .04248 Mdot .44095 .05999 Mdot .44119 .30646 Mdot .44143 .55527 Mdot .44167 .57768 Mdot .4419 .35308 Mdot .44214 .08797 Mdot .44238 .02609 Mdot .44262 .22433 Mdot .44286 .50043 Mdot .4431 .60055 Mdot .44333 .43263 Mdot .44357 .15106 Mdot .44381 .01472 Mdot .44405 .14895 Mdot .44429 .43035 Mdot .44452 .6002 Mdot .44476 .50234 Mdot .445 .22674 Mdot .44524 .02679 Mdot .44548 .08632 Mdot .44571 .35059 Mdot .44595 .57665 Mdot .44619 .55664 Mdot .44643 .30897 Mdot .44667 .06134 Mdot .4469 .04143 Mdot .44714 .26753 Mdot .44738 .53178 Mdot .44762 .59122 Mdot .44786 .39121 Mdot .4481 .11563 Mdot .44833 .01785 Mdot .44857 .18777 Mdot .44881 .46916 Mdot .44905 .60332 Mdot .44929 .4669 Mdot .44952 .18532 Mdot .44976 .01747 Mdot .45 .11767 Mdot .45024 .39379 Mdot .45048 .59197 Mdot .45071 .53001 Mdot .45095 .26486 Mdot .45119 .04032 Mdot .45143 .06281 Mdot .45167 .31167 Mdot .4519 .55809 Mdot .45214 .57551 Mdot .45238 .34792 Mdot .45262 .08456 Mdot .45286 .02756 Mdot .4531 .22933 Mdot .45333 .50436 Mdot .45357 .59979 Mdot .45381 .42789 Mdot .45405 .14669 Mdot .45429 .01474 Mdot .45452 .15334 Mdot .45476 .43507 Mdot .455 .60091 Mdot .45524 .49838 Mdot .45548 .22175 Mdot .45571 .02536 Mdot .45595 .08976 Mdot .45619 .35574 Mdot .45643 .57877 Mdot .45667 .55379 Mdot .4569 .30376 Mdot .45714 .05857 Mdot .45738 .04364 Mdot .45762 .27269 Mdot .45786 .53515 Mdot .4581 .5897 Mdot .45833 .38619 Mdot .45857 .11173 Mdot .45881 .01866 Mdot .45905 .19254 Mdot .45929 .47351 Mdot .45952 .60325 Mdot .45976 .46247 Mdot .46 .18061 Mdot .46024 .0168 Mdot .46048 .12166 Mdot .46071 .39877 Mdot .46095 .59336 Mdot .46119 .52653 Mdot .46143 .25972 Mdot .46167 .03823 Mdot .4619 .0657 Mdot .46214 .31688 Mdot .46238 .56082 Mdot .46262 .57326 Mdot .46286 .34275 Mdot .4631 .08123 Mdot .46333 .02913 Mdot .46357 .23436 Mdot .46381 .50823 Mdot .46405 .59894 Mdot .46429 .4231 Mdot .46452 .14237 Mdot .46476 .01486 Mdot .465 .15779 Mdot .46524 .43976 Mdot .46548 .60153 Mdot .46571 .49436 Mdot .46595 .21679 Mdot .46619 .02401 Mdot .46643 .09327 Mdot .46667 .36088 Mdot .4669 .58081 Mdot .46714 .55086 Mdot .46738 .29855 Mdot .46762 .05587 Mdot .46786 .04593 Mdot .4681 .27787 Mdot .46833 .53845 Mdot .46857 .58809 Mdot .46881 .38115 Mdot .46905 .1079 Mdot .46929 .01955 Mdot .46952 .19734 Mdot .46976 .4778 Mdot .47 .60309 Mdot .47024 .458 Mdot .47048 .17594 Mdot .47071 .01623 Mdot .47095 .1257 Mdot .47119 .40371 Mdot .47143 .59466 Mdot .47167 .52299 Mdot .4719 .25459 Mdot .47214 .03623 Mdot .47238 .06867 Mdot .47262 .32208 Mdot .47286 .56348 Mdot .4731 .57093 Mdot .47333 .33757 Mdot .47357 .07797 Mdot .47381 .03079 Mdot .47405 .23941 Mdot .47429 .51203 Mdot .47452 .598 Mdot .47476 .41828 Mdot .475 .1381 Mdot .47524 .01506 Mdot .47548 .16228 Mdot .47571 .44441 Mdot .47595 .60206 Mdot .47619 .49029 Mdot .47643 .21186 Mdot .47667 .02276 Mdot .4769 .09684 Mdot .47714 .366 Mdot .47738 .58277 Mdot .47762 .54785 Mdot .47786 .29335 Mdot .4781 .05325 Mdot .47833 .04831 Mdot .47857 .28305 Mdot .47881 .54167 Mdot .47905 .58639 Mdot .47929 .37609 Mdot .47952 .10413 Mdot .47976 .02054 Mdot .48 .20218 Mdot .48024 .48204 Mdot .48048 .60283 Mdot .48071 .45349 Mdot .48095 .17132 Mdot .48119 .01575 Mdot .48143 .12981 Mdot .48167 .40863 Mdot .4819 .59587 Mdot .48214 .51938 Mdot .48238 .24948 Mdot .48262 .03432 Mdot .48286 .07172 Mdot .4831 .32728 Mdot .48333 .56606 Mdot .48357 .56851 Mdot .48381 .33238 Mdot .48405 .07478 Mdot .48429 .03253 Mdot .48452 .24448 Mdot .48476 .51577 Mdot .485 .59697 Mdot .48524 .41343 Mdot .48548 .13389 Mdot .48571 .01536 Mdot .48595 .16682 Mdot .48619 .44901 Mdot .48643 .60249 Mdot .48667 .48615 Mdot .4869 .20695 Mdot .48714 .02159 Mdot .48738 .10049 Mdot .48762 .3711 Mdot .48786 .58464 Mdot .4881 .54477 Mdot .48833 .28815 Mdot .48857 .05072 Mdot .48881 .05076 Mdot .48905 .28825 Mdot .48929 .54483 Mdot .48952 .5846 Mdot .48976 .37101 Mdot .49 .10042 Mdot .49024 .02161 Mdot .49048 .20705 Mdot .49071 .48623 Mdot .49095 .60249 Mdot .49119 .44893 Mdot .49143 .16674 Mdot .49167 .01536 Mdot .4919 .13397 Mdot .49214 .41352 Mdot .49238 .59699 Mdot .49262 .5157 Mdot .49286 .24439 Mdot .4931 .03249 Mdot .49333 .07483 Mdot .49357 .33248 Mdot .49381 .56856 Mdot .49405 .56601 Mdot .49429 .32719 Mdot .49452 .07166 Mdot .49476 .03436 Mdot .495 .24958 Mdot .49524 .51945 Mdot .49548 .59585 Mdot .49571 .40854 Mdot .49595 .12973 Mdot .49619 .01576 Mdot .49643 .1714 Mdot .49667 .45357 Mdot .4969 .60284 Mdot .49714 .48196 Mdot .49738 .20208 Mdot .49762 .02052 Mdot .49786 .1042 Mdot .4981 .37619 Mdot .49833 .58642 Mdot .49857 .54161 Mdot .49881 .28296 Mdot .49905 .04826 Mdot .49929 .0533 Mdot .49952 .29345 Mdot .49976 .54791 Mdot .5 .58273 Mdot .50024 .3659 Mdot .50048 .09678 Mdot .50071 .02278 Mdot .50095 .21195 Mdot .50119 .49036 Mdot .50143 .60205 Mdot .50167 .44432 Mdot .5019 .1622 Mdot .50214 .01506 Mdot .50238 .13818 Mdot .50262 .41837 Mdot .50286 .59802 Mdot .5031 .51196 Mdot .50333 .23931 Mdot .50357 .03075 Mdot .50381 .07803 Mdot .50405 .33767 Mdot .50429 .57097 Mdot .50452 .56343 Mdot .50476 .32198 Mdot .505 .06862 Mdot .50524 .03627 Mdot .50548 .25469 Mdot .50571 .52305 Mdot .50595 .59464 Mdot .50619 .40362 Mdot .50643 .12563 Mdot .50667 .01624 Mdot .5069 .17603 Mdot .50714 .45809 Mdot .50738 .60309 Mdot .50762 .47772 Mdot .50786 .19725 Mdot .5081 .01953 Mdot .50833 .10797 Mdot .50857 .38125 Mdot .50881 .58812 Mdot .50905 .53838 Mdot .50929 .27777 Mdot .50952 .04589 Mdot .50976 .05592 Mdot .51 .29865 Mdot .51024 .55091 Mdot .51048 .58077 Mdot .51071 .36078 Mdot .51095 .0932 Mdot .51119 .02404 Mdot .51143 .21688 Mdot .51167 .49444 Mdot .5119 .60152 Mdot .51214 .43967 Mdot .51238 .15771 Mdot .51262 .01485 Mdot .51286 .14245 Mdot .5131 .42319 Mdot .51333 .59896 Mdot .51357 .50815 Mdot .51381 .23426 Mdot .51405 .0291 Mdot .51429 .08129 Mdot .51452 .34285 Mdot .51476 .5733 Mdot .515 .56077 Mdot .51524 .31678 Mdot .51548 .06565 Mdot .51571 .03827 Mdot .51595 .25982 Mdot .51619 .5266 Mdot .51643 .59334 Mdot .51667 .39867 Mdot .5169 .12158 Mdot .51714 .01682 Mdot .51738 .1807 Mdot .51762 .46256 Mdot .51786 .60325 Mdot .5181 .47343 Mdot .51833 .19245 Mdot .51857 .01864 Mdot .51881 .11181 Mdot .51905 .38629 Mdot .51929 .58973 Mdot .51952 .53508 Mdot .51976 .2726 Mdot .52 .04359 Mdot .52024 .05862 Mdot .52048 .30386 Mdot .52071 .55384 Mdot .52095 .57873 Mdot .52119 .35565 Mdot .52143 .08969 Mdot .52167 .02538 Mdot .5219 .22185 Mdot .52214 .49845 Mdot .52238 .6009 Mdot .52262 .43498 Mdot .52286 .15326 Mdot .5231 .01474 Mdot .52333 .14677 Mdot .52357 .42798 Mdot .52381 .59981 Mdot .52405 .50429 Mdot .52429 .22924 Mdot .52452 .02754 Mdot .52476 .08463 Mdot .525 .34802 Mdot .52524 .57556 Mdot .52548 .55804 Mdot .52571 .31157 Mdot .52595 .06276 Mdot .52619 .04035 Mdot .52643 .26496 Mdot .52667 .53007 Mdot .5269 .59195 Mdot .52714 .3937 Mdot .52738 .11759 Mdot .52762 .01748 Mdot .52786 .18541 Mdot .5281 .46698 Mdot .52833 .60332 Mdot .52857 .46908 Mdot .52881 .18768 Mdot .52905 .01784 Mdot .52929 .1157 Mdot .52952 .3913 Mdot .52976 .59125 Mdot .53 .53171 Mdot .53024 .26743 Mdot .53048 .04138 Mdot .53071 .0614 Mdot .53095 .30907 Mdot .53119 .55669 Mdot .53143 .57661 Mdot .53167 .3505 Mdot .5319 .08625 Mdot .53214 .02682 Mdot .53238 .22683 Mdot .53262 .50241 Mdot .53286 .60018 Mdot .5331 .43026 Mdot .53333 .14886 Mdot .53357 .01472 Mdot .53381 .15115 Mdot .53405 .43272 Mdot .53429 .60056 Mdot .53452 .50036 Mdot .53476 .22423 Mdot .535 .02606 Mdot .53524 .08803 Mdot .53548 .35318 Mdot .53571 .57772 Mdot .53595 .55522 Mdot .53619 .30636 Mdot .53643 .05994 Mdot .53667 .04252 Mdot .5369 .27012 Mdot .53714 .53348 Mdot .53738 .59047 Mdot .53762 .38869 Mdot .53786 .11367 Mdot .5381 .01824 Mdot .53833 .19016 Mdot .53857 .47135 Mdot .53881 .60329 Mdot .53905 .46468 Mdot .53929 .18295 Mdot .53952 .01713 Mdot .53976 .11966 Mdot .54 .39629 Mdot .54024 .59268 Mdot .54048 .52827 Mdot .54071 .26228 Mdot .54095 .03926 Mdot .54119 .06425 Mdot .54143 .31428 Mdot .54167 .55947 Mdot .5419 .57439 Mdot .54214 .34533 Mdot .54238 .08288 Mdot .54262 .02834 Mdot .54286 .23185 Mdot .5431 .50631 Mdot .54333 .59938 Mdot .54357 .42549 Mdot .54381 .14452 Mdot .54405 .01479 Mdot .54429 .15557 Mdot .54452 .43743 Mdot .54476 .60123 Mdot .545 .49637 Mdot .54524 .21926 Mdot .54548 .02467 Mdot .54571 .09151 Mdot .54595 .35832 Mdot .54619 .57981 Mdot .54643 .55233 Mdot .54667 .30115 Mdot .5469 .05721 Mdot .54714 .04478 Mdot .54738 .27529 Mdot .54762 .53681 Mdot .54786 .5889 Mdot .5481 .38367 Mdot .54833 .1098 Mdot .54857 .01909 Mdot .54881 .19494 Mdot .54905 .47567 Mdot .54929 .60318 Mdot .54952 .46024 Mdot .54976 .17827 Mdot .55 .01651 Mdot .55024 .12368 Mdot .55048 .40125 Mdot .55071 .59402 Mdot .55095 .52476 Mdot .55119 .25714 Mdot .55143 .03722 Mdot .55167 .06718 Mdot .5519 .31949 Mdot .55214 .56217 Mdot .55238 .5721 Mdot .55262 .34016 Mdot .55286 .07958 Mdot .5531 .02995 Mdot .55333 .23689 Mdot .55357 .51014 Mdot .55381 .59848 Mdot .55405 .42069 Mdot .55429 .14022 Mdot .55452 .01495 Mdot .55476 .16004 Mdot .555 .4421 Mdot .55524 .6018 Mdot .55548 .49232 Mdot .55571 .21431 Mdot .55595 .02337 Mdot .55619 .09505 Mdot .55643 .36345 Mdot .55667 .5818 Mdot .5569 .54936 Mdot .55714 .29594 Mdot .55738 .05455 Mdot .55762 .04711 Mdot .55786 .28047 Mdot .5581 .54007 Mdot .55833 .58725 Mdot .55857 .37862 Mdot .55881 .106 Mdot .55905 .02003 Mdot .55929 .19976 Mdot .55952 .47994 Mdot .55976 .60297 Mdot .56 .45574 Mdot .56024 .17362 Mdot .56048 .01598 Mdot .56071 .12776 Mdot .56095 .40619 Mdot .56119 .59528 Mdot .56143 .52118 Mdot .56167 .25202 Mdot .5619 .03526 Mdot .56214 .07019 Mdot .56238 .32469 Mdot .56262 .56478 Mdot .56286 .56972 Mdot .5631 .33497 Mdot .56333 .07636 Mdot .56357 .03165 Mdot .56381 .24195 Mdot .56405 .51391 Mdot .56429 .5975 Mdot .56452 .41585 Mdot .56476 .13598 Mdot .565 .0152 Mdot .56524 .16455 Mdot .56548 .44672 Mdot .56571 .60229 Mdot .56595 .48822 Mdot .56619 .20939 Mdot .56643 .02216 Mdot .56667 .09866 Mdot .5669 .36856 Mdot .56714 .58372 Mdot .56738 .54631 Mdot .56762 .29074 Mdot .56786 .05197 Mdot .5681 .04953 Mdot .56833 .28566 Mdot .56857 .54326 Mdot .56881 .5855 Mdot .56905 .37354 Mdot .56929 .10226 Mdot .56952 .02107 Mdot .56976 .20462 Mdot .57 .48415 Mdot .57024 .60267 Mdot .57048 .45121 Mdot .57071 .16901 Mdot .57095 .01554 Mdot .57119 .13189 Mdot .57143 .41109 Mdot .57167 .59644 Mdot .5719 .51754 Mdot .57214 .24692 Mdot .57238 .03339 Mdot .57262 .07327 Mdot .57286 .32989 Mdot .5731 .56732 Mdot .57333 .56727 Mdot .57357 .32978 Mdot .57381 .0732 Mdot .57405 .03343 Mdot .57429 .24704 Mdot .57452 .51762 Mdot .57476 .59642 Mdot .575 .41098 Mdot .57524 .1318 Mdot .57548 .01555 Mdot .57571 .16912 Mdot .57595 .45131 Mdot .57619 .60268 Mdot .57643 .48406 Mdot .57667 .20451 Mdot .5769 .02104 Mdot .57714 .10234 Mdot .57738 .37366 Mdot .57762 .58554 Mdot .57786 .54319 Mdot .5781 .28554 Mdot .57833 .04947 Mdot .57857 .05203 Mdot .57881 .29086 Mdot .57905 .54638 Mdot .57929 .58368 Mdot .57952 .36845 Mdot .57976 .09858 Mdot .58 .02219 Mdot .58024 .2095 Mdot .58048 .48831 Mdot .58071 .60228 Mdot .58095 .44662 Mdot .58119 .16445 Mdot .58143 .0152 Mdot .58167 .13608 Mdot .5819 .41596 Mdot .58214 .59752 Mdot .58238 .51383 Mdot .58262 .24184 Mdot .58286 .03161 Mdot .5831 .07643 Mdot .58333 .33509 Mdot .58357 .56978 Mdot .58381 .56473 Mdot .58405 .32458 Mdot .58429 .07012 Mdot .58452 .03531 Mdot .58476 .25214 Mdot .585 .52126 Mdot .58524 .59525 Mdot .58548 .40608 Mdot .58571 .12766 Mdot .58595 .01599 Mdot .58619 .17372 Mdot .58643 .45584 Mdot .58667 .60298 Mdot .5869 .47984 Mdot .58714 .19965 Mdot .58738 .02001 Mdot .58762 .10608 Mdot .58786 .37873 Mdot .5881 .58728 Mdot .58833 .54 Mdot .58857 .28035 Mdot .58881 .04706 Mdot .58905 .05461 Mdot .58929 .29606 Mdot .58952 .54942 Mdot .58976 .58176 Mdot .59 .36334 Mdot .59024 .09497 Mdot .59048 .0234 Mdot .59071 .21442 Mdot .59095 .49241 Mdot .59119 .60179 Mdot .59143 .44199 Mdot .59167 .15994 Mdot .5919 .01494 Mdot .59214 .14032 Mdot .59238 .42079 Mdot .59262 .5985 Mdot .59286 .51006 Mdot .5931 .23678 Mdot .59333 .02991 Mdot .59357 .07966 Mdot .59381 .34027 Mdot .59405 .57215 Mdot .59429 .56211 Mdot .59452 .31937 Mdot .59476 .06712 Mdot .595 .03726 Mdot .59524 .25726 Mdot .59548 .52484 Mdot .59571 .594 Mdot .59595 .40114 Mdot .59619 .12359 Mdot .59643 .01652 Mdot .59667 .17837 Mdot .5969 .46034 Mdot .59714 .60318 Mdot .59738 .47557 Mdot .59762 .19483 Mdot .59786 .01907 Mdot .5981 .10989 Mdot .59833 .38378 Mdot .59857 .58894 Mdot .59881 .53674 Mdot .59905 .27517 Mdot .59929 .04473 Mdot .59952 .05727 Mdot .59976 .30126 Mdot .6 .55239 Mdot .60024 .57976 Mdot .60048 .35821 Mdot .60071 .09143 Mdot .60095 .0247 Mdot .60119 .21937 Mdot .60143 .49646 Mdot .60167 .60122 Mdot .6019 .43733 Mdot .60214 .15547 Mdot .60238 .01478 Mdot .60262 .14461 Mdot .60286 .4256 Mdot .6031 .5994 Mdot .60333 .50622 Mdot .60357 .23174 Mdot .60381 .0283 Mdot .60405 .08296 Mdot .60429 .34545 Mdot .60452 .57444 Mdot .60476 .55941 Mdot .605 .31416 Mdot .60524 .06419 Mdot .60548 .03931 Mdot .60571 .26239 Mdot .60595 .52835 Mdot .60619 .59265 Mdot .60643 .39618 Mdot .60667 .11957 Mdot .6069 .01714 Mdot .60714 .18306 Mdot .60738 .46478 Mdot .60762 .6033 Mdot .60786 .47125 Mdot .6081 .19005 Mdot .60833 .01823 Mdot .60857 .11375 Mdot .60881 .38881 Mdot .60905 .5905 Mdot .60929 .5334 Mdot .60952 .27 Mdot .60976 .04247 Mdot .61 .06 Mdot .61024 .30647 Mdot .61048 .55528 Mdot .61071 .57768 Mdot .61095 .35307 Mdot .61119 .08796 Mdot .61143 .02609 Mdot .61167 .22435 Mdot .6119 .50045 Mdot .61214 .60055 Mdot .61238 .43262 Mdot .61262 .15105 Mdot .61286 .01472 Mdot .6131 .14896 Mdot .61333 .43036 Mdot .61357 .6002 Mdot .61381 .50232 Mdot .61405 .22672 Mdot .61429 .02678 Mdot .61452 .08633 Mdot .61476 .35061 Mdot .615 .57665 Mdot .61524 .55663 Mdot .61548 .30895 Mdot .61571 .06133 Mdot .61595 .04143 Mdot .61619 .26755 Mdot .61643 .53179 Mdot .61667 .59122 Mdot .6169 .39119 Mdot .61714 .11562 Mdot .61738 .01785 Mdot .61762 .18779 Mdot .61786 .46918 Mdot .6181 .60332 Mdot .61833 .46688 Mdot .61857 .1853 Mdot .61881 .01747 Mdot .61905 .11768 Mdot .61929 .39381 Mdot .61952 .59198 Mdot .61976 .52999 Mdot .62 .26485 Mdot .62024 .04031 Mdot .62048 .06282 Mdot .62071 .31168 Mdot .62095 .5581 Mdot .62119 .57551 Mdot .62143 .34791 Mdot .62167 .08455 Mdot .6219 .02757 Mdot .62214 .22935 Mdot .62238 .50437 Mdot .62262 .59979 Mdot .62286 .42787 Mdot .6231 .14668 Mdot .62333 .01474 Mdot .62357 .15336 Mdot .62381 .43509 Mdot .62405 .60091 Mdot .62429 .49837 Mdot .62452 .22174 Mdot .62476 .02535 Mdot .625 .08977 Mdot .62524 .35576 Mdot .62548 .57878 Mdot .62571 .55378 Mdot .62595 .30375 Mdot .62619 .05856 Mdot .62643 .04364 Mdot .62667 .27271 Mdot .6269 .53516 Mdot .62714 .58969 Mdot .62738 .38618 Mdot .62762 .11172 Mdot .62786 .01866 Mdot .6281 .19255 Mdot .62833 .47352 Mdot .62857 .60325 Mdot .62881 .46246 Mdot .62905 .1806 Mdot .62929 .0168 Mdot .62952 .12167 Mdot .62976 .39878 Mdot .63 .59337 Mdot .63024 .52652 Mdot .63048 .2597 Mdot .63071 .03822 Mdot .63095 .06571 Mdot .63119 .31689 Mdot .63143 .56083 Mdot .63167 .57325 Mdot .6319 .34274 Mdot .63214 .08122 Mdot .63238 .02914 Mdot .63262 .23438 Mdot .63286 .50824 Mdot .6331 .59894 Mdot .63333 .42309 Mdot .63357 .14236 Mdot .63381 .01486 Mdot .63405 .1578 Mdot .63429 .43978 Mdot .63452 .60153 Mdot .63476 .49435 Mdot .635 .21677 Mdot .63524 .02401 Mdot .63548 .09328 Mdot .63571 .3609 Mdot .63595 .58082 Mdot .63619 .55085 Mdot .63643 .29854 Mdot .63667 .05586 Mdot .6369 .04594 Mdot .63714 .27789 Mdot .63738 .53846 Mdot .63762 .58808 Mdot .63786 .38114 Mdot .6381 .10788 Mdot .63833 .01955 Mdot .63857 .19735 Mdot .63881 .47782 Mdot .63905 .60309 Mdot .63929 .45799 Mdot .63952 .17593 Mdot .63976 .01623 Mdot .64 .12572 Mdot .64024 .40373 Mdot .64048 .59466 Mdot .64071 .52298 Mdot .64095 .25457 Mdot .64119 .03623 Mdot .64143 .06868 Mdot .64167 .3221 Mdot .6419 .56349 Mdot .64214 .57092 Mdot .64238 .33756 Mdot .64262 .07796 Mdot .64286 .03079 Mdot .6431 .23943 Mdot .64333 .51204 Mdot .64357 .598 Mdot .64381 .41827 Mdot .64405 .13809 Mdot .64429 .01506 Mdot .64452 .1623 Mdot .64476 .44442 Mdot .645 .60206 Mdot .64524 .49027 Mdot .64548 .21184 Mdot .64571 .02275 Mdot .64595 .09686 Mdot .64619 .36602 Mdot .64643 .58277 Mdot .64667 .54784 Mdot .6469 .29333 Mdot .64714 .05325 Mdot .64738 .04831 Mdot .64762 .28307 Mdot .64786 .54168 Mdot .6481 .58638 Mdot .64833 .37607 Mdot .64857 .10411 Mdot .64881 .02054 Mdot .64905 .20219 Mdot .64929 .48206 Mdot .64952 .60283 Mdot .64976 .45347 Mdot .65 .1713 Mdot .65024 .01575 Mdot .65048 .12982 Mdot .65071 .40865 Mdot .65095 .59587 Mdot .65119 .51936 Mdot .65143 .24946 Mdot .65167 .03431 Mdot .6519 .07173 Mdot .65214 .3273 Mdot .65238 .56607 Mdot .65262 .5685 Mdot .65286 .33237 Mdot .6531 .07476 Mdot .65333 .03253 Mdot .65357 .2445 Mdot .65381 .51578 Mdot .65405 .59697 Mdot .65429 .41341 Mdot .65452 .13388 Mdot .65476 .01537 Mdot .655 .16684 Mdot .65524 .44903 Mdot .65548 .60249 Mdot .65571 .48614 Mdot .65595 .20694 Mdot .65619 .02159 Mdot .65643 .1005 Mdot .65667 .37112 Mdot .6569 .58464 Mdot .65714 .54476 Mdot .65738 .28813 Mdot .65762 .05071 Mdot .65786 .05077 Mdot .6581 .28827 Mdot .65833 .54484 Mdot .65857 .5846 Mdot .65881 .37099 Mdot .65905 .10041 Mdot .65929 .02162 Mdot .65952 .20706 Mdot .65976 .48624 Mdot .66 .60248 Mdot .66024 .44891 Mdot .66048 .16672 Mdot .66071 .01536 Mdot .66095 .13398 Mdot .66119 .41353 Mdot .66143 .59699 Mdot .66167 .51569 Mdot .6619 .24437 Mdot .66214 .03249 Mdot .66238 .07485 Mdot .66262 .3325 Mdot .66286 .56856 Mdot .6631 .566 Mdot .66333 .32717 Mdot .66357 .07165 Mdot .66381 .03436 Mdot .66405 .24959 Mdot .66429 .51946 Mdot .66452 .59584 Mdot .66476 .40852 Mdot .665 .12972 Mdot .66524 .01576 Mdot .66548 .17142 Mdot .66571 .45359 Mdot .66595 .60284 Mdot .66619 .48195 Mdot .66643 .20207 Mdot .66667 .02051 Mdot .6669 .10421 Mdot .66714 .3762 Mdot .66738 .58643 Mdot .66762 .5416 Mdot .66786 .28294 Mdot .6681 .04825 Mdot .66833 .05331 Mdot .66857 .29347 Mdot .66881 .54792 Mdot .66905 .58273 Mdot .66929 .36589 Mdot .66952 .09676 Mdot .66976 .02278 Mdot .67 .21197 Mdot .67024 .49038 Mdot .67048 .60205 Mdot .67071 .44431 Mdot .67095 .16218 Mdot .67119 .01506 Mdot .67143 .1382 Mdot .67167 .41839 Mdot .6719 .59802 Mdot .67214 .51195 Mdot .67238 .2393 Mdot .67262 .03075 Mdot .67286 .07804 Mdot .6731 .33769 Mdot .67333 .57098 Mdot .67357 .56342 Mdot .67381 .32197 Mdot .67405 .06861 Mdot .67429 .03628 Mdot .67452 .2547 Mdot .67476 .52307 Mdot .675 .59463 Mdot .67524 .4036 Mdot .67548 .12561 Mdot .67571 .01624 Mdot .67595 .17605 Mdot .67619 .4581 Mdot .67643 .60309 Mdot .67667 .47771 Mdot .6769 .19723 Mdot .67714 .01953 Mdot .67738 .10798 Mdot .67762 .38126 Mdot .67786 .58812 Mdot .6781 .53837 Mdot .67833 .27775 Mdot .67857 .04588 Mdot .67881 .05593 Mdot .67905 .29867 Mdot .67929 .55092 Mdot .67952 .58077 Mdot .67976 .36077 Mdot .68 .09319 Mdot .68024 .02404 Mdot .68048 .2169 Mdot .68071 .49445 Mdot .68095 .60151 Mdot .68119 .43966 Mdot .68143 .15769 Mdot .68167 .01485 Mdot .6819 .14247 Mdot .68214 .42321 Mdot .68238 .59896 Mdot .68262 .50814 Mdot .68286 .23425 Mdot .6831 .0291 Mdot .68333 .0813 Mdot .68357 .34287 Mdot .68381 .57331 Mdot .68405 .56076 Mdot .68429 .31676 Mdot .68452 .06564 Mdot .68476 .03828 Mdot .685 .25983 Mdot .68524 .52661 Mdot .68548 .59333 Mdot .68571 .39866 Mdot .68595 .12157 Mdot .68619 .01682 Mdot .68643 .18072 Mdot .68667 .46257 Mdot .6869 .60325 Mdot .68714 .47341 Mdot .68738 .19243 Mdot .68762 .01864 Mdot .68786 .11182 Mdot .6881 .3863 Mdot .68833 .58973 Mdot .68857 .53507 Mdot .68881 .27258 Mdot .68905 .04359 Mdot .68929 .05863 Mdot .68952 .30388 Mdot .68976 .55385 Mdot .69 .57872 Mdot .69024 .35563 Mdot .69048 .08968 Mdot .69071 .02539 Mdot .69095 .22186 Mdot .69119 .49847 Mdot .69143 .60089 Mdot .69167 .43497 Mdot .6919 .15325 Mdot .69214 .01474 Mdot .69238 .14679 Mdot .69262 .42799 Mdot .69286 .59981 Mdot .6931 .50427 Mdot .69333 .22922 Mdot .69357 .02753 Mdot .69381 .08464 Mdot .69405 .34804 Mdot .69429 .57556 Mdot .69452 .55803 Mdot .69476 .31155 Mdot .695 .06275 Mdot .69524 .04036 Mdot .69548 .26498 Mdot .69571 .53008 Mdot .69595 .59194 Mdot .69619 .39368 Mdot .69643 .11758 Mdot .69667 .01749 Mdot .6969 .18542 Mdot .69714 .46699 Mdot .69738 .60332 Mdot .69762 .46907 Mdot .69786 .18766 Mdot .6981 .01783 Mdot .69833 .11572 Mdot .69857 .39132 Mdot .69881 .59125 Mdot .69905 .5317 Mdot .69929 .26741 Mdot .69952 .04138 Mdot .69976 .06141 Mdot .7 .30909 Mdot .70024 .5567 Mdot .70048 .5766 Mdot .70071 .35048 Mdot .70095 .08624 Mdot .70119 .02682 Mdot .70143 .22685 Mdot .70167 .50242 Mdot .7019 .60018 Mdot .70214 .43024 Mdot .70238 .14885 Mdot .70262 .01472 Mdot .70286 .15116 Mdot .7031 .43274 Mdot .70333 .60057 Mdot .70357 .50035 Mdot .70381 .22422 Mdot .70405 .02605 Mdot .70429 .08805 Mdot .70452 .3532 Mdot .70476 .57773 Mdot .705 .55521 Mdot .70524 .30634 Mdot .70548 .05993 Mdot .70571 .04253 Mdot .70595 .27014 Mdot .70619 .53349 Mdot .70643 .59046 Mdot .70667 .38868 Mdot .7069 .11365 Mdot .70714 .01825 Mdot .70738 .19017 Mdot .70762 .47136 Mdot .70786 .60329 Mdot .7081 .46467 Mdot .70833 .18294 Mdot .70857 .01712 Mdot .70881 .11968 Mdot .70905 .39631 Mdot .70929 .59269 Mdot .70952 .52826 Mdot .70976 .26226 Mdot .71 .03925 Mdot .71024 .06426 Mdot .71048 .3143 Mdot .71071 .55948 Mdot .71095 .57439 Mdot .71119 .34531 Mdot .71143 .08287 Mdot .71167 .02834 Mdot .7119 .23187 Mdot .71214 .50632 Mdot .71238 .59937 Mdot .71262 .42547 Mdot .71286 .1445 Mdot .7131 .01479 Mdot .71333 .15558 Mdot .71357 .43745 Mdot .71381 .60123 Mdot .71405 .49636 Mdot .71429 .21924 Mdot .71452 .02467 Mdot .71476 .09152 Mdot .715 .35834 Mdot .71524 .57981 Mdot .71548 .55232 Mdot .71571 .30113 Mdot .71595 .0572 Mdot .71619 .04478 Mdot .71643 .27531 Mdot .71667 .53682 Mdot .7169 .58889 Mdot .71714 .38365 Mdot .71738 .10979 Mdot .71762 .0191 Mdot .71786 .19496 Mdot .7181 .47568 Mdot .71833 .60318 Mdot .71857 .46022 Mdot .71881 .17825 Mdot .71905 .0165 Mdot .71929 .12369 Mdot .71952 .40127 Mdot .71976 .59403 Mdot .72 .52475 Mdot .72024 .25713 Mdot .72048 .03721 Mdot .72071 .06719 Mdot .72095 .31951 Mdot .72119 .56218 Mdot .72143 .57209 Mdot .72167 .34014 Mdot .7219 .07957 Mdot .72214 .02996 Mdot .72238 .23691 Mdot .72262 .51016 Mdot .72286 .59848 Mdot .7231 .42067 Mdot .72333 .14021 Mdot .72357 .01495 Mdot .72381 .16005 Mdot .72405 .44211 Mdot .72429 .60181 Mdot .72452 .49231 Mdot .72476 .21429 Mdot .725 .02337 Mdot .72524 .09506 Mdot .72548 .36347 Mdot .72571 .58181 Mdot .72595 .54935 Mdot .72619 .29593 Mdot .72643 .05454 Mdot .72667 .04712 Mdot .7269 .28049 Mdot .72714 .54008 Mdot .72738 .58724 Mdot .72762 .3786 Mdot .72786 .10598 Mdot .7281 .02004 Mdot .72833 .19978 Mdot .72857 .47995 Mdot .72881 .60297 Mdot .72905 .45573 Mdot .72929 .1736 Mdot .72952 .01598 Mdot .72976 .12777 Mdot .73 .4062 Mdot .73024 .59528 Mdot .73048 .52117 Mdot .73071 .25201 Mdot .73095 .03526 Mdot .73119 .0702 Mdot .73143 .32471 Mdot .73167 .56479 Mdot .7319 .56972 Mdot .73214 .33495 Mdot .73238 .07635 Mdot .73262 .03165 Mdot .73286 .24197 Mdot .7331 .51393 Mdot .73333 .59749 Mdot .73357 .41583 Mdot .73381 .13597 Mdot .73405 .0152 Mdot .73429 .16457 Mdot .73452 .44674 Mdot .73476 .60229 Mdot .735 .48821 Mdot .73524 .20938 Mdot .73548 .02216 Mdot .73571 .09868 Mdot .73595 .36858 Mdot .73619 .58372 Mdot .73643 .5463 Mdot .73667 .29072 Mdot .7369 .05196 Mdot .73714 .04954 Mdot .73738 .28568 Mdot .73762 .54327 Mdot .73786 .5855 Mdot .7381 .37353 Mdot .73833 .10224 Mdot .73857 .02107 Mdot .73881 .20463 Mdot .73905 .48417 Mdot .73929 .60267 Mdot .73952 .45119 Mdot .73976 .169 Mdot .74 .01554 Mdot .74024 .1319 Mdot .74048 .4111 Mdot .74071 .59645 Mdot .74095 .51753 Mdot .74119 .24691 Mdot .74143 .03339 Mdot .74167 .07328 Mdot .7419 .32991 Mdot .74214 .56733 Mdot .74238 .56726 Mdot .74262 .32976 Mdot .74286 .07319 Mdot .7431 .03344 Mdot .74333 .24705 Mdot .74357 .51763 Mdot .74381 .59641 Mdot .74405 .41096 Mdot .74429 .13178 Mdot .74452 .01555 Mdot .74476 .16913 Mdot .745 .45132 Mdot .74524 .60268 Mdot .74548 .48404 Mdot .74571 .20449 Mdot .74595 .02104 Mdot .74619 .10235 Mdot .74643 .37367 Mdot .74667 .58555 Mdot .7469 .54318 Mdot .74714 .28553 Mdot .74738 .04947 Mdot .74762 .05204 Mdot .74786 .29087 Mdot .7481 .54639 Mdot .74833 .58367 Mdot .74857 .36843 Mdot .74881 .09857 Mdot .74905 .02219 Mdot .74929 .20952 Mdot .74952 .48832 Mdot .74976 .60228 Mdot .75 .44661 Mdot .75024 .16444 Mdot .75048 .0152 Mdot .75071 .13609 Mdot .75095 .41597 Mdot .75119 .59752 Mdot .75143 .51382 Mdot .75167 .24182 Mdot .7519 .0316 Mdot .75214 .07644 Mdot .75238 .3351 Mdot .75262 .56979 Mdot .75286 .56472 Mdot .7531 .32456 Mdot .75333 .07011 Mdot .75357 .03531 Mdot .75381 .25216 Mdot .75405 .52128 Mdot .75429 .59525 Mdot .75452 .40606 Mdot .75476 .12765 Mdot .755 .01599 Mdot .75524 .17374 Mdot .75548 .45586 Mdot .75571 .60298 Mdot .75595 .47983 Mdot .75619 .19964 Mdot .75643 .02001 Mdot .75667 .10609 Mdot .7569 .37875 Mdot .75714 .58729 Mdot .75738 .53999 Mdot .75762 .28034 Mdot .75786 .04705 Mdot .7581 .05462 Mdot .75833 .29608 Mdot .75857 .54943 Mdot .75881 .58175 Mdot .75905 .36332 Mdot .75929 .09496 Mdot .75952 .0234 Mdot .75976 .21444 Mdot .76 .49243 Mdot .76024 .60179 Mdot .76048 .44198 Mdot .76071 .15992 Mdot .76095 .01494 Mdot .76119 .14033 Mdot .76143 .42081 Mdot .76167 .59851 Mdot .7619 .51005 Mdot .76214 .23676 Mdot .76238 .02991 Mdot .76262 .07967 Mdot .76286 .34029 Mdot .7631 .57216 Mdot .76333 .5621 Mdot .76357 .31936 Mdot .76381 .06711 Mdot .76405 .03727 Mdot .76429 .25728 Mdot .76452 .52485 Mdot .76476 .59399 Mdot .765 .40113 Mdot .76524 .12358 Mdot .76548 .01652 Mdot .76571 .17838 Mdot .76595 .46035 Mdot .76619 .60318 Mdot .76643 .47556 Mdot .76667 .19482 Mdot .7669 .01907 Mdot .76714 .1099 Mdot .76738 .3838 Mdot .76762 .58894 Mdot .76786 .53673 Mdot .7681 .27516 Mdot .76833 .04472 Mdot .76857 .05728 Mdot .76881 .30128 Mdot .76905 .5524 Mdot .76929 .57975 Mdot .76952 .35819 Mdot .76976 .09142 Mdot .77 .0247 Mdot .77024 .21939 Mdot .77048 .49647 Mdot .77071 .60121 Mdot .77095 .43731 Mdot .77119 .15545 Mdot .77143 .01478 Mdot .77167 .14463 Mdot .7719 .42561 Mdot .77214 .5994 Mdot .77238 .50621 Mdot .77262 .23172 Mdot .77286 .0283 Mdot .7731 .08297 Mdot .77333 .34546 Mdot .77357 .57445 Mdot .77381 .5594 Mdot .77405 .31415 Mdot .77429 .06418 Mdot .77452 .03931 Mdot .77476 .26241 Mdot .775 .52836 Mdot .77524 .59264 Mdot .77548 .39616 Mdot .77571 .11956 Mdot .77595 .01714 Mdot .77619 .18307 Mdot .77643 .4648 Mdot .77667 .6033 Mdot .7769 .47124 Mdot .77714 .19003 Mdot .77738 .01822 Mdot .77762 .11377 Mdot .77786 .38882 Mdot .7781 .59051 Mdot .77833 .53339 Mdot .77857 .26999 Mdot .77881 .04247 Mdot .77905 .06001 Mdot .77929 .30649 Mdot .77952 .55529 Mdot .77976 .57767 Mdot .78 .35305 Mdot .78024 .08795 Mdot .78048 .0261 Mdot .78071 .22436 Mdot .78095 .50046 Mdot .78119 .60055 Mdot .78143 .4326 Mdot .78167 .15103 Mdot .7819 .01472 Mdot .78214 .14898 Mdot .78238 .43038 Mdot .78262 .6002 Mdot .78286 .50231 Mdot .7831 .22671 Mdot .78333 .02678 Mdot .78357 .08634 Mdot .78381 .35063 Mdot .78405 .57666 Mdot .78429 .55662 Mdot .78452 .30894 Mdot .78476 .06133 Mdot .785 .04144 Mdot .78524 .26756 Mdot .78548 .5318 Mdot .78571 .59121 Mdot .78595 .39117 Mdot .78619 .1156 Mdot .78643 .01786 Mdot .78667 .1878 Mdot .7869 .46919 Mdot .78714 .60332 Mdot .78738 .46687 Mdot .78762 .18529 Mdot .78786 .01747 Mdot .7881 .1177 Mdot .78833 .39382 Mdot .78857 .59198 Mdot .78881 .52998 Mdot .78905 .26483 Mdot .78929 .0403 Mdot .78952 .06283 Mdot .78976 .3117 Mdot .79 .55811 Mdot .79024 .5755 Mdot .79048 .34789 Mdot .79071 .08454 Mdot .79095 .02757 Mdot .79119 .22937 Mdot .79143 .50439 Mdot .79167 .59979 Mdot .7919 .42785 Mdot .79214 .14666 Mdot .79238 .01474 Mdot .79262 .15337 Mdot .79286 .43511 Mdot .7931 .60091 Mdot .79333 .49835 Mdot .79357 .22172 Mdot .79381 .02535 Mdot .79405 .08978 Mdot .79429 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Doch Folgen mit unendlich vielen Werten sind \ prinzipiell ", StyleBox["nicht", FontWeight->"Bold"], " grafisch darstellbar und entziehen sich dadurch unserer Anschauung. 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Betrachtet werden Anfangsst\[UDoubleDot]cke der Folge \ ", Cell[BoxData[ \(TraditionalForm\`\((\[NegativeThinSpace]\ \((\(-1\))\)\^n\/n\ \ \[NegativeThinSpace])\)\)]], " . Zu den Werten \[CurlyEpsilon] = 0.1, 0.01, 0.001 ist um Null jeweils \ ein hellgrauer Streifen von \[Dash]\[CurlyEpsilon] bis \[CurlyEpsilon] \ gelegt. Es sieht so aus, als ob die Folgenglieder schlie\[SZ]lich alle in \ diesem \"\[CurlyEpsilon]-Streifen drinliegen\" bzw. die Folgenglieder dem \ Wert Null \"recht nahe kommen\".\n" }], "Text"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Symbol %%IncludeFont: Symbol /Symbol findfont 12 scalefont setfont % Scaling calculations 6.93889e-018 0.0333333 0.258005 0.690628 [ [-0.0125 .25807 -19 -8.3125 ] [-0.0125 .25807 0 8.3125 ] [-0.0125 .18887 -26.4375 -8.3125 ] [-0.0125 .18887 0 8.3125 ] [-0.0125 .32714 -18.75 -8.3125 ] [-0.0125 .32714 0 8.3125 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .258 m 1 .258 L s 0 .25807 m .00625 .25807 L s gsave -0.0125 .25807 -80 -12.3125 Mabsadd 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Mdot .241 .20205 Mdot .24133 .41591 Mdot .24167 .20234 Mdot .242 .41561 Mdot .24233 .20264 Mdot .24267 .41532 Mdot .243 .20293 Mdot .24333 .41503 Mdot .24367 .20322 Mdot .244 .41474 Mdot .24433 .20351 Mdot .24467 .41445 Mdot .245 .20379 Mdot .24533 .41417 Mdot .24567 .20408 Mdot .246 .41388 Mdot .24633 .20436 Mdot .24667 .4136 Mdot .247 .20465 Mdot .24733 .41332 Mdot .24767 .20493 Mdot .248 .41304 Mdot .24833 .20521 Mdot .24867 .41276 Mdot .249 .20548 Mdot .24933 .41248 Mdot .24967 .20576 Mdot .25 .4122 Mdot .25033 .20604 Mdot .25067 .41193 Mdot .251 .20631 Mdot .25133 .41166 Mdot .25167 .20658 Mdot .252 .41139 Mdot .25233 .20685 Mdot .25267 .41112 Mdot .253 .20712 Mdot .25333 .41085 Mdot .25367 .20739 Mdot .254 .41058 Mdot .25433 .20766 Mdot .25467 .41031 Mdot .255 .20792 Mdot .25533 .41005 Mdot .25567 .20819 Mdot .256 .40979 Mdot .25633 .20845 Mdot .25667 .40953 Mdot .257 .20871 Mdot .25733 .40927 Mdot .25767 .20897 Mdot .258 .40901 Mdot .25833 .20923 Mdot .25867 .40875 Mdot .259 .20948 Mdot .25933 .40849 Mdot .25967 .20974 Mdot .26 .40824 Mdot .26033 .20999 Mdot .26067 .40798 Mdot .261 .21025 Mdot .26133 .40773 Mdot .26167 .2105 Mdot .262 .40748 Mdot .26233 .21075 Mdot .26267 .40723 Mdot .263 .211 Mdot .26333 .40698 Mdot .26367 .21125 Mdot .264 .40673 Mdot .26433 .21149 Mdot .26467 .40649 Mdot .265 .21174 Mdot .26533 .40624 Mdot .26567 .21198 Mdot .266 .406 Mdot .26633 .21223 Mdot .26667 .40576 Mdot .267 .21247 Mdot .26733 .40552 Mdot .26767 .21271 Mdot .268 .40528 Mdot .26833 .21295 Mdot .26867 .40504 Mdot .269 .21319 Mdot .26933 .4048 Mdot .26967 .21342 Mdot .27 .40456 Mdot .27033 .21366 Mdot .27067 .40433 Mdot .271 .21389 Mdot .27133 .40409 Mdot .27167 .21413 Mdot .272 .40386 Mdot .27233 .21436 Mdot .27267 .40363 Mdot .273 .21459 Mdot .27333 .4034 Mdot .27367 .21482 Mdot .274 .40317 Mdot .27433 .21505 Mdot .27467 .40294 Mdot .275 .21528 Mdot .27533 .40271 Mdot .27567 .2155 Mdot .276 .40249 Mdot .27633 .21573 Mdot .27667 .40226 Mdot .277 .21595 Mdot .27733 .40204 Mdot .27767 .21618 Mdot .278 .40182 Mdot .27833 .2164 Mdot .27867 .40159 Mdot .279 .21662 Mdot .27933 .40137 Mdot .27967 .21684 Mdot .28 .40115 Mdot .28033 .21706 Mdot .28067 .40093 Mdot .281 .21728 Mdot .28133 .40072 Mdot .28167 .2175 Mdot .282 .4005 Mdot .28233 .21771 Mdot .28267 .40028 Mdot .283 .21793 Mdot .28333 .40007 Mdot .28367 .21814 Mdot .284 .39986 Mdot .28433 .21835 Mdot .28467 .39964 Mdot .285 .21857 Mdot .28533 .39943 Mdot .28567 .21878 Mdot .286 .39922 Mdot .28633 .21899 Mdot .28667 .39901 Mdot .287 .2192 Mdot .28733 .3988 Mdot .28767 .21941 Mdot .288 .39859 Mdot .28833 .21961 Mdot .28867 .39839 Mdot .289 .21982 Mdot .28933 .39818 Mdot .28967 .22002 Mdot .29 .39798 Mdot .29033 .22023 Mdot .29067 .39777 Mdot .291 .22043 Mdot .29133 .39757 Mdot .29167 .22064 Mdot .292 .39737 Mdot .29233 .22084 Mdot .29267 .39717 Mdot .293 .22104 Mdot .29333 .39697 Mdot .29367 .22124 Mdot .294 .39677 Mdot .29433 .22144 Mdot .29467 .39657 Mdot .295 .22163 Mdot .29533 .39637 Mdot .29567 .22183 Mdot .296 .39617 Mdot .29633 .22203 Mdot .29667 .39598 Mdot .297 .22222 Mdot .29733 .39578 Mdot .29767 .22242 Mdot .298 .39559 Mdot .29833 .22261 Mdot .29867 .3954 Mdot .299 .2228 Mdot .29933 .3952 Mdot .29967 .223 Mdot .3 .39501 Mdot .30033 .22319 Mdot .30067 .39482 Mdot .301 .22338 Mdot .30133 .39463 Mdot .30167 .22357 Mdot .302 .39444 Mdot .30233 .22375 Mdot .30267 .39426 Mdot .303 .22394 Mdot .30333 .39407 Mdot .30367 .22413 Mdot .304 .39388 Mdot .30433 .22432 Mdot .30467 .3937 Mdot .305 .2245 Mdot .30533 .39351 Mdot .30567 .22468 Mdot .306 .39333 Mdot .30633 .22487 Mdot .30667 .39314 Mdot .307 .22505 Mdot .30733 .39296 Mdot .30767 .22523 Mdot .308 .39278 Mdot .30833 .22541 Mdot .30867 .3926 Mdot .309 .2256 Mdot .30933 .39242 Mdot .30967 .22577 Mdot .31 .39224 Mdot .31033 .22595 Mdot .31067 .39206 Mdot .311 .22613 Mdot .31133 .39188 Mdot .31167 .22631 Mdot .312 .39171 Mdot .31233 .22649 Mdot .31267 .39153 Mdot .313 .22666 Mdot .31333 .39135 Mdot .31367 .22684 Mdot .314 .39118 Mdot .31433 .22701 Mdot .31467 .39101 Mdot .315 .22718 Mdot .31533 .39083 Mdot .31567 .22736 Mdot .316 .39066 Mdot .31633 .22753 Mdot .31667 .39049 Mdot .317 .2277 Mdot .31733 .39032 Mdot .31767 .22787 Mdot .318 .39015 Mdot .31833 .22804 Mdot .31867 .38998 Mdot .319 .22821 Mdot .31933 .38981 Mdot .31967 .22838 Mdot .32 .38964 Mdot .32033 .22855 Mdot .32067 .38947 Mdot .321 .22871 Mdot .32133 .38931 Mdot .32167 .22888 Mdot .322 .38914 Mdot .32233 .22905 Mdot .32267 .38897 Mdot .323 .22921 Mdot .32333 .38881 Mdot .32367 .22938 Mdot .324 .38865 Mdot .32433 .22954 Mdot .32467 .38848 Mdot .325 .2297 Mdot .32533 .38832 Mdot .32567 .22987 Mdot .326 .38816 Mdot .32633 .23003 Mdot .32667 .388 Mdot .327 .23019 Mdot .32733 .38783 Mdot .32767 .23035 Mdot .328 .38767 Mdot .32833 .23051 Mdot .32867 .38752 Mdot .329 .23067 Mdot .32933 .38736 Mdot .32967 .23083 Mdot .33 .3872 Mdot .33033 .23098 Mdot .33067 .38704 Mdot .331 .23114 Mdot .33133 .38688 Mdot .33167 .2313 Mdot .332 .38673 Mdot .33233 .23145 Mdot .33267 .38657 Mdot .333 .23161 Mdot .33333 .38642 Mdot .33367 .23176 Mdot .334 .38626 Mdot .33433 .23192 Mdot .33467 .38611 Mdot .335 .23207 Mdot .33533 .38596 Mdot .33567 .23223 Mdot .336 .3858 Mdot .33633 .23238 Mdot .33667 .38565 Mdot .337 .23253 Mdot .33733 .3855 Mdot .33767 .23268 Mdot .338 .38535 Mdot .33833 .23283 Mdot .33867 .3852 Mdot .339 .23298 Mdot .33933 .38505 Mdot .33967 .23313 Mdot .34 .3849 Mdot .34033 .23328 Mdot .34067 .38475 Mdot .341 .23343 Mdot .34133 .3846 Mdot .34167 .23357 Mdot .342 .38446 Mdot .34233 .23372 Mdot .34267 .38431 Mdot .343 .23387 Mdot .34333 .38416 Mdot .34367 .23401 Mdot .344 .38402 Mdot .34433 .23416 Mdot .34467 .38387 Mdot .345 .2343 Mdot .34533 .38373 Mdot .34567 .23445 Mdot .346 .38358 Mdot .34633 .23459 Mdot .34667 .38344 Mdot .347 .23473 Mdot .34733 .3833 Mdot .34767 .23488 Mdot .348 .38316 Mdot .34833 .23502 Mdot .34867 .38301 Mdot .349 .23516 Mdot .34933 .38287 Mdot .34967 .2353 Mdot .35 .38273 Mdot .35033 .23544 Mdot .35067 .38259 Mdot .351 .23558 Mdot .35133 .38245 Mdot .35167 .23572 Mdot .352 .38231 Mdot .35233 .23586 Mdot .35267 .38218 Mdot .353 .236 Mdot .35333 .38204 Mdot .35367 .23614 Mdot .354 .3819 Mdot .35433 .23627 Mdot .35467 .38176 Mdot .355 .23641 Mdot .35533 .38163 Mdot .35567 .23655 Mdot .356 .38149 Mdot .35633 .23668 Mdot .35667 .38136 Mdot .357 .23682 Mdot .35733 .38122 Mdot .35767 .23695 Mdot .358 .38109 Mdot .35833 .23708 Mdot .35867 .38095 Mdot .359 .23722 Mdot .35933 .38082 Mdot .35967 .23735 Mdot .36 .38069 Mdot .36033 .23748 Mdot .36067 .38055 Mdot .361 .23762 Mdot .36133 .38042 Mdot .36167 .23775 Mdot .362 .38029 Mdot .36233 .23788 Mdot .36267 .38016 Mdot .363 .23801 Mdot .36333 .38003 Mdot .36367 .23814 Mdot .364 .3799 Mdot .36433 .23827 Mdot .36467 .37977 Mdot .365 .2384 Mdot .36533 .37964 Mdot .36567 .23853 Mdot .366 .37951 Mdot .36633 .23866 Mdot .36667 .37938 Mdot .367 .23878 Mdot .36733 .37926 Mdot .36767 .23891 Mdot .368 .37913 Mdot .36833 .23904 Mdot .36867 .379 Mdot .369 .23917 Mdot .36933 .37888 Mdot .36967 .23929 Mdot .37 .37875 Mdot .37033 .23942 Mdot .37067 .37862 Mdot .371 .23954 Mdot .37133 .3785 Mdot .37167 .23967 Mdot .372 .37838 Mdot .37233 .23979 Mdot .37267 .37825 Mdot .373 .23991 Mdot .37333 .37813 Mdot .37367 .24004 Mdot .374 .378 Mdot .37433 .24016 Mdot .37467 .37788 Mdot .375 .24028 Mdot .37533 .37776 Mdot .37567 .24041 Mdot .376 .37764 Mdot .37633 .24053 Mdot .37667 .37752 Mdot .377 .24065 Mdot .37733 .3774 Mdot .37767 .24077 Mdot .378 .37727 Mdot .37833 .24089 Mdot .37867 .37715 Mdot .379 .24101 Mdot .37933 .37703 Mdot .37967 .24113 Mdot .38 .37692 Mdot .38033 .24125 Mdot .38067 .3768 Mdot .381 .24137 Mdot .38133 .37668 Mdot .38167 .24148 Mdot .382 .37656 Mdot .38233 .2416 Mdot .38267 .37644 Mdot .383 .24172 Mdot .38333 .37633 Mdot .38367 .24184 Mdot .384 .37621 Mdot .38433 .24195 Mdot .38467 .37609 Mdot .385 .24207 Mdot .38533 .37598 Mdot .38567 .24219 Mdot .386 .37586 Mdot .38633 .2423 Mdot .38667 .37575 Mdot .387 .24242 Mdot .38733 .37563 Mdot .38767 .24253 Mdot .388 .37552 Mdot .38833 .24264 Mdot .38867 .3754 Mdot .389 .24276 Mdot .38933 .37529 Mdot .38967 .24287 Mdot .39 .37518 Mdot .39033 .24298 Mdot .39067 .37506 Mdot .391 .2431 Mdot .39133 .37495 Mdot .39167 .24321 Mdot .392 .37484 Mdot .39233 .24332 Mdot .39267 .37473 Mdot .393 .24343 Mdot .39333 .37462 Mdot .39367 .24354 Mdot .394 .3745 Mdot .39433 .24366 Mdot .39467 .37439 Mdot .395 .24377 Mdot .39533 .37428 Mdot .39567 .24388 Mdot .396 .37417 Mdot .39633 .24399 Mdot .39667 .37406 Mdot .397 .24409 Mdot .39733 .37396 Mdot .39767 .2442 Mdot .398 .37385 Mdot .39833 .24431 Mdot .39867 .37374 Mdot .399 .24442 Mdot .39933 .37363 Mdot .39967 .24453 Mdot .4 .37352 Mdot .40033 .24464 Mdot .40067 .37342 Mdot .401 .24474 Mdot .40133 .37331 Mdot .40167 .24485 Mdot .402 .3732 Mdot .40233 .24496 Mdot .40267 .3731 Mdot .403 .24506 Mdot .40333 .37299 Mdot .40367 .24517 Mdot .404 .37288 Mdot .40433 .24527 Mdot .40467 .37278 Mdot .405 .24538 Mdot .40533 .37267 Mdot .40567 .24548 Mdot .406 .37257 Mdot .40633 .24559 Mdot .40667 .37247 Mdot .407 .24569 Mdot .40733 .37236 Mdot .40767 .24579 Mdot .408 .37226 Mdot .40833 .2459 Mdot .40867 .37216 Mdot .409 .246 Mdot .40933 .37205 Mdot .40967 .2461 Mdot .41 .37195 Mdot .41033 .24621 Mdot .41067 .37185 Mdot .411 .24631 Mdot .41133 .37175 Mdot .41167 .24641 Mdot .412 .37164 Mdot .41233 .24651 Mdot .41267 .37154 Mdot .413 .24661 Mdot .41333 .37144 Mdot .41367 .24671 Mdot .414 .37134 Mdot .41433 .24681 Mdot .41467 .37124 Mdot .415 .24691 Mdot .41533 .37114 Mdot .41567 .24701 Mdot .416 .37104 Mdot .41633 .24711 Mdot .41667 .37094 Mdot .417 .24721 Mdot .41733 .37084 Mdot .41767 .24731 Mdot .418 .37075 Mdot .41833 .24741 Mdot .41867 .37065 Mdot .419 .2475 Mdot .41933 .37055 Mdot .41967 .2476 Mdot .42 .37045 Mdot .42033 .2477 Mdot .42067 .37036 Mdot .421 .2478 Mdot .42133 .37026 Mdot .42167 .24789 Mdot .422 .37016 Mdot .42233 .24799 Mdot .42267 .37007 Mdot .423 .24809 Mdot .42333 .36997 Mdot .42367 .24818 Mdot .424 .36987 Mdot .42433 .24828 Mdot .42467 .36978 Mdot .425 .24837 Mdot .42533 .36968 Mdot .42567 .24847 Mdot .426 .36959 Mdot .42633 .24856 Mdot .42667 .36949 Mdot .427 .24866 Mdot .42733 .3694 Mdot .42767 .24875 Mdot .428 .3693 Mdot .42833 .24885 Mdot .42867 .36921 Mdot .429 .24894 Mdot .42933 .36912 Mdot .42967 .24903 Mdot .43 .36902 Mdot .43033 .24913 Mdot .43067 .36893 Mdot .431 .24922 Mdot .43133 .36884 Mdot .43167 .24931 Mdot .432 .36875 Mdot .43233 .2494 Mdot .43267 .36865 Mdot .433 .24949 Mdot .43333 .36856 Mdot .43367 .24959 Mdot .434 .36847 Mdot .43433 .24968 Mdot .43467 .36838 Mdot .435 .24977 Mdot .43533 .36829 Mdot .43567 .24986 Mdot .436 .3682 Mdot .43633 .24995 Mdot .43667 .36811 Mdot .437 .25004 Mdot .43733 .36802 Mdot .43767 .25013 Mdot .438 .36793 Mdot .43833 .25022 Mdot .43867 .36784 Mdot .439 .25031 Mdot .43933 .36775 Mdot .43967 .2504 Mdot .44 .36766 Mdot .44033 .25049 Mdot .44067 .36757 Mdot .441 .25058 Mdot .44133 .36748 Mdot .44167 .25066 Mdot .442 .3674 Mdot .44233 .25075 Mdot .44267 .36731 Mdot .443 .25084 Mdot .44333 .36722 Mdot .44367 .25093 Mdot .444 .36713 Mdot .44433 .25101 Mdot .44467 .36705 Mdot .445 .2511 Mdot .44533 .36696 Mdot .44567 .25119 Mdot .446 .36687 Mdot .44633 .25127 Mdot .44667 .36679 Mdot .447 .25136 Mdot .44733 .3667 Mdot .44767 .25145 Mdot .448 .36661 Mdot .44833 .25153 Mdot .44867 .36653 Mdot .449 .25162 Mdot .44933 .36644 Mdot .44967 .2517 Mdot .45 .36636 Mdot .45033 .25179 Mdot .45067 .36627 Mdot .451 .25187 Mdot .45133 .36619 Mdot .45167 .25196 Mdot .452 .36611 Mdot .45233 .25204 Mdot .45267 .36602 Mdot .453 .25212 Mdot .45333 .36594 Mdot .45367 .25221 Mdot .454 .36585 Mdot .45433 .25229 Mdot .45467 .36577 Mdot .455 .25237 Mdot .45533 .36569 Mdot .45567 .25246 Mdot .456 .36561 Mdot .45633 .25254 Mdot .45667 .36552 Mdot .457 .25262 Mdot .45733 .36544 Mdot .45767 .2527 Mdot .458 .36536 Mdot .45833 .25279 Mdot .45867 .36528 Mdot .459 .25287 Mdot .45933 .36519 Mdot .45967 .25295 Mdot .46 .36511 Mdot .46033 .25303 Mdot .46067 .36503 Mdot .461 .25311 Mdot .46133 .36495 Mdot .46167 .25319 Mdot .462 .36487 Mdot .46233 .25327 Mdot .46267 .36479 Mdot .463 .25335 Mdot .46333 .36471 Mdot .46367 .25343 Mdot .464 .36463 Mdot .46433 .25351 Mdot .46467 .36455 Mdot .465 .25359 Mdot .46533 .36447 Mdot .46567 .25367 Mdot .466 .36439 Mdot .46633 .25375 Mdot .46667 .36431 Mdot .467 .25383 Mdot .46733 .36423 Mdot .46767 .25391 Mdot .468 .36415 Mdot .46833 .25399 Mdot .46867 .36408 Mdot .469 .25407 Mdot .46933 .364 Mdot .46967 .25414 Mdot .47 .36392 Mdot .47033 .25422 Mdot .47067 .36384 Mdot .471 .2543 Mdot .47133 .36377 Mdot .47167 .25438 Mdot .472 .36369 Mdot .47233 .25445 Mdot .47267 .36361 Mdot .473 .25453 Mdot .47333 .36353 Mdot .47367 .25461 Mdot .474 .36346 Mdot .47433 .25468 Mdot .47467 .36338 Mdot .475 .25476 Mdot .47533 .3633 Mdot .47567 .25484 Mdot .476 .36323 Mdot .47633 .25491 Mdot .47667 .36315 Mdot .477 .25499 Mdot .47733 .36308 Mdot .47767 .25506 Mdot .478 .363 Mdot .47833 .25514 Mdot .47867 .36293 Mdot .479 .25521 Mdot .47933 .36285 Mdot .47967 .25529 Mdot .48 .36278 Mdot .48033 .25536 Mdot .48067 .3627 Mdot .481 .25544 Mdot .48133 .36263 Mdot .48167 .25551 Mdot .482 .36255 Mdot .48233 .25559 Mdot .48267 .36248 Mdot .483 .25566 Mdot .48333 .36241 Mdot .48367 .25573 Mdot .484 .36233 Mdot .48433 .25581 Mdot .48467 .36226 Mdot .485 .25588 Mdot .48533 .36219 Mdot .48567 .25595 Mdot .486 .36211 Mdot .48633 .25603 Mdot .48667 .36204 Mdot .487 .2561 Mdot .48733 .36197 Mdot .48767 .25617 Mdot .488 .3619 Mdot .48833 .25624 Mdot .48867 .36182 Mdot .489 .25632 Mdot .48933 .36175 Mdot .48967 .25639 Mdot .49 .36168 Mdot .49033 .25646 Mdot .49067 .36161 Mdot .491 .25653 Mdot .49133 .36154 Mdot .49167 .2566 Mdot .492 .36147 Mdot .49233 .25667 Mdot .49267 .3614 Mdot .493 .25674 Mdot .49333 .36133 Mdot .49367 .25681 Mdot .494 .36125 Mdot .49433 .25688 Mdot .49467 .36118 Mdot .495 .25695 Mdot .49533 .36111 Mdot .49567 .25702 Mdot .496 .36104 Mdot .49633 .25709 Mdot .49667 .36097 Mdot .497 .25716 Mdot .49733 .3609 Mdot .49767 .25723 Mdot .498 .36084 Mdot .49833 .2573 Mdot .49867 .36077 Mdot .499 .25737 Mdot .49933 .3607 Mdot .49967 .25744 Mdot .5 .36063 Mdot .50033 .25751 Mdot .50067 .36056 Mdot .501 .25758 Mdot .50133 .36049 Mdot .50167 .25765 Mdot .502 .36042 Mdot .50233 .25772 Mdot .50267 .36035 Mdot .503 .25778 Mdot .50333 .36029 Mdot .50367 .25785 Mdot .504 .36022 Mdot .50433 .25792 Mdot .50467 .36015 Mdot .505 .25799 Mdot .50533 .36008 Mdot .50567 .25805 Mdot .506 .36002 Mdot .50633 .25812 Mdot .50667 .35995 Mdot .507 .25819 Mdot .50733 .35988 Mdot .50767 .25825 Mdot .508 .35982 Mdot .50833 .25832 Mdot .50867 .35975 Mdot .509 .25839 Mdot .50933 .35968 Mdot .50967 .25845 Mdot .51 .35962 Mdot .51033 .25852 Mdot .51067 .35955 Mdot .511 .25859 Mdot .51133 .35949 Mdot .51167 .25865 Mdot .512 .35942 Mdot .51233 .25872 Mdot .51267 .35935 Mdot .513 .25878 Mdot .51333 .35929 Mdot .51367 .25885 Mdot .514 .35922 Mdot .51433 .25891 Mdot .51467 .35916 Mdot .515 .25898 Mdot .51533 .35909 Mdot .51567 .25904 Mdot .516 .35903 Mdot .51633 .25911 Mdot .51667 .35896 Mdot .517 .25917 Mdot .51733 .3589 Mdot .51767 .25924 Mdot .518 .35884 Mdot .51833 .2593 Mdot .51867 .35877 Mdot .519 .25936 Mdot .51933 .35871 Mdot .51967 .25943 Mdot .52 .35864 Mdot .52033 .25949 Mdot .52067 .35858 Mdot .521 .25955 Mdot .52133 .35852 Mdot .52167 .25962 Mdot .522 .35845 Mdot .52233 .25968 Mdot .52267 .35839 Mdot .523 .25974 Mdot .52333 .35833 Mdot .52367 .25981 Mdot .524 .35827 Mdot .52433 .25987 Mdot .52467 .3582 Mdot .525 .25993 Mdot .52533 .35814 Mdot .52567 .25999 Mdot .526 .35808 Mdot .52633 .26006 Mdot .52667 .35802 Mdot .527 .26012 Mdot .52733 .35796 Mdot .52767 .26018 Mdot .528 .35789 Mdot .52833 .26024 Mdot .52867 .35783 Mdot .529 .2603 Mdot .52933 .35777 Mdot .52967 .26036 Mdot .53 .35771 Mdot .53033 .26043 Mdot .53067 .35765 Mdot .531 .26049 Mdot .53133 .35759 Mdot .53167 .26055 Mdot .532 .35753 Mdot .53233 .26061 Mdot .53267 .35747 Mdot .533 .26067 Mdot .53333 .3574 Mdot .53367 .26073 Mdot .534 .35734 Mdot .53433 .26079 Mdot .53467 .35728 Mdot .535 .26085 Mdot .53533 .35722 Mdot .53567 .26091 Mdot .536 .35716 Mdot .53633 .26097 Mdot .53667 .3571 Mdot .537 .26103 Mdot .53733 .35704 Mdot .53767 .26109 Mdot .538 .35699 Mdot .53833 .26115 Mdot .53867 .35693 Mdot .539 .26121 Mdot .53933 .35687 Mdot .53967 .26127 Mdot .54 .35681 Mdot .54033 .26133 Mdot .54067 .35675 Mdot .541 .26138 Mdot .54133 .35669 Mdot .54167 .26144 Mdot .542 .35663 Mdot .54233 .2615 Mdot .54267 .35657 Mdot .543 .26156 Mdot .54333 .35651 Mdot .54367 .26162 Mdot .544 .35646 Mdot .54433 .26168 Mdot .54467 .3564 Mdot .545 .26173 Mdot .54533 .35634 Mdot .54567 .26179 Mdot .546 .35628 Mdot .54633 .26185 Mdot .54667 .35623 Mdot .547 .26191 Mdot .54733 .35617 Mdot .54767 .26196 Mdot .548 .35611 Mdot .54833 .26202 Mdot .54867 .35605 Mdot .549 .26208 Mdot .54933 .356 Mdot .54967 .26214 Mdot .55 .35594 Mdot .55033 .26219 Mdot .55067 .35588 Mdot .551 .26225 Mdot .55133 .35583 Mdot .55167 .26231 Mdot .552 .35577 Mdot .55233 .26236 Mdot .55267 .35571 Mdot .553 .26242 Mdot .55333 .35566 Mdot .55367 .26247 Mdot .554 .3556 Mdot .55433 .26253 Mdot .55467 .35555 Mdot .555 .26259 Mdot .55533 .35549 Mdot .55567 .26264 Mdot .556 .35543 Mdot .55633 .2627 Mdot .55667 .35538 Mdot .557 .26275 Mdot .55733 .35532 Mdot .55767 .26281 Mdot .558 .35527 Mdot .55833 .26286 Mdot .55867 .35521 Mdot .559 .26292 Mdot .55933 .35516 Mdot .55967 .26297 Mdot .56 .3551 Mdot .56033 .26303 Mdot .56067 .35505 Mdot .561 .26308 Mdot .56133 .35499 Mdot .56167 .26314 Mdot .562 .35494 Mdot .56233 .26319 Mdot .56267 .35488 Mdot .563 .26325 Mdot .56333 .35483 Mdot .56367 .2633 Mdot .564 .35478 Mdot .56433 .26336 Mdot .56467 .35472 Mdot .565 .26341 Mdot .56533 .35467 Mdot .56567 .26346 Mdot .566 .35461 Mdot .56633 .26352 Mdot .56667 .35456 Mdot .567 .26357 Mdot .56733 .35451 Mdot .56767 .26362 Mdot .568 .35445 Mdot .56833 .26368 Mdot .56867 .3544 Mdot .569 .26373 Mdot .56933 .35435 Mdot .56967 .26378 Mdot .57 .35429 Mdot .57033 .26384 Mdot .57067 .35424 Mdot .571 .26389 Mdot .57133 .35419 Mdot .57167 .26394 Mdot .572 .35414 Mdot .57233 .26399 Mdot .57267 .35408 Mdot .573 .26405 Mdot .57333 .35403 Mdot .57367 .2641 Mdot .574 .35398 Mdot .57433 .26415 Mdot .57467 .35393 Mdot .575 .2642 Mdot .57533 .35388 Mdot .57567 .26425 Mdot .576 .35382 Mdot .57633 .26431 Mdot .57667 .35377 Mdot .577 .26436 Mdot .57733 .35372 Mdot .57767 .26441 Mdot .578 .35367 Mdot .57833 .26446 Mdot .57867 .35362 Mdot .579 .26451 Mdot .57933 .35357 Mdot .57967 .26456 Mdot .58 .35351 Mdot .58033 .26462 Mdot .58067 .35346 Mdot .581 .26467 Mdot .58133 .35341 Mdot .58167 .26472 Mdot .582 .35336 Mdot .58233 .26477 Mdot .58267 .35331 Mdot .583 .26482 Mdot .58333 .35326 Mdot .58367 .26487 Mdot .584 .35321 Mdot .58433 .26492 Mdot .58467 .35316 Mdot .585 .26497 Mdot .58533 .35311 Mdot .58567 .26502 Mdot .586 .35306 Mdot .58633 .26507 Mdot .58667 .35301 Mdot .587 .26512 Mdot .58733 .35296 Mdot .58767 .26517 Mdot .588 .35291 Mdot .58833 .26522 Mdot .58867 .35286 Mdot .589 .26527 Mdot .58933 .35281 Mdot .58967 .26532 Mdot .59 .35276 Mdot .59033 .26537 Mdot .59067 .35271 Mdot .591 .26542 Mdot .59133 .35266 Mdot .59167 .26547 Mdot .592 .35261 Mdot .59233 .26552 Mdot .59267 .35256 Mdot .593 .26556 Mdot .59333 .35252 Mdot .59367 .26561 Mdot .594 .35247 Mdot .59433 .26566 Mdot .59467 .35242 Mdot .595 .26571 Mdot .59533 .35237 Mdot .59567 .26576 Mdot .596 .35232 Mdot .59633 .26581 Mdot .59667 .35227 Mdot .597 .26586 Mdot .59733 .35222 Mdot .59767 .2659 Mdot .598 .35218 Mdot .59833 .26595 Mdot .59867 .35213 Mdot .599 .266 Mdot .59933 .35208 Mdot .59967 .26605 Mdot .6 .35203 Mdot .60033 .2661 Mdot .60067 .35198 Mdot .601 .26614 Mdot .60133 .35194 Mdot .60167 .26619 Mdot .602 .35189 Mdot .60233 .26624 Mdot .60267 .35184 Mdot .603 .26629 Mdot .60333 .35179 Mdot .60367 .26633 Mdot .604 .35175 Mdot .60433 .26638 Mdot .60467 .3517 Mdot .605 .26643 Mdot .60533 .35165 Mdot .60567 .26647 Mdot .606 .35161 Mdot .60633 .26652 Mdot .60667 .35156 Mdot .607 .26657 Mdot .60733 .35151 Mdot .60767 .26661 Mdot .608 .35147 Mdot .60833 .26666 Mdot .60867 .35142 Mdot .609 .26671 Mdot .60933 .35137 Mdot .60967 .26675 Mdot .61 .35133 Mdot .61033 .2668 Mdot .61067 .35128 Mdot .611 .26685 Mdot .61133 .35124 Mdot .61167 .26689 Mdot .612 .35119 Mdot .61233 .26694 Mdot .61267 .35114 Mdot .613 .26698 Mdot .61333 .3511 Mdot .61367 .26703 Mdot .614 .35105 Mdot .61433 .26707 Mdot .61467 .35101 Mdot .615 .26712 Mdot .61533 .35096 Mdot .61567 .26717 Mdot .616 .35092 Mdot .61633 .26721 Mdot .61667 .35087 Mdot .617 .26726 Mdot .61733 .35083 Mdot .61767 .2673 Mdot .618 .35078 Mdot .61833 .26735 Mdot .61867 .35074 Mdot .619 .26739 Mdot .61933 .35069 Mdot .61967 .26744 Mdot .62 .35065 Mdot .62033 .26748 Mdot .62067 .3506 Mdot .621 .26753 Mdot .62133 .35056 Mdot .62167 .26757 Mdot .622 .35051 Mdot .62233 .26761 Mdot .62267 .35047 Mdot .623 .26766 Mdot .62333 .35042 Mdot .62367 .2677 Mdot .624 .35038 Mdot .62433 .26775 Mdot .62467 .35034 Mdot .625 .26779 Mdot .62533 .35029 Mdot .62567 .26783 Mdot .626 .35025 Mdot .62633 .26788 Mdot .62667 .3502 Mdot .627 .26792 Mdot .62733 .35016 Mdot .62767 .26797 Mdot .628 .35012 Mdot .62833 .26801 Mdot .62867 .35007 Mdot .629 .26805 Mdot .62933 .35003 Mdot .62967 .2681 Mdot .63 .34999 Mdot .63033 .26814 Mdot .63067 .34994 Mdot .631 .26818 Mdot .63133 .3499 Mdot .63167 .26823 Mdot .632 .34986 Mdot .63233 .26827 Mdot .63267 .34981 Mdot .633 .26831 Mdot .63333 .34977 Mdot .63367 .26836 Mdot .634 .34973 Mdot .63433 .2684 Mdot .63467 .34968 Mdot .635 .26844 Mdot .63533 .34964 Mdot .63567 .26848 Mdot .636 .3496 Mdot .63633 .26853 Mdot .63667 .34956 Mdot .637 .26857 Mdot .63733 .34951 Mdot .63767 .26861 Mdot .638 .34947 Mdot .63833 .26865 Mdot .63867 .34943 Mdot .639 .26869 Mdot .63933 .34939 Mdot .63967 .26874 Mdot .64 .34935 Mdot .64033 .26878 Mdot .64067 .3493 Mdot .641 .26882 Mdot .64133 .34926 Mdot .64167 .26886 Mdot .642 .34922 Mdot .64233 .2689 Mdot .64267 .34918 Mdot .643 .26895 Mdot .64333 .34914 Mdot .64367 .26899 Mdot .644 .3491 Mdot .64433 .26903 Mdot .64467 .34905 Mdot .645 .26907 Mdot .64533 .34901 Mdot .64567 .26911 Mdot .646 .34897 Mdot .64633 .26915 Mdot .64667 .34893 Mdot .647 .26919 Mdot .64733 .34889 Mdot .64767 .26923 Mdot .648 .34885 Mdot .64833 .26928 Mdot .64867 .34881 Mdot .649 .26932 Mdot .64933 .34877 Mdot .64967 .26936 Mdot .65 .34873 Mdot .65033 .2694 Mdot .65067 .34869 Mdot .651 .26944 Mdot .65133 .34864 Mdot .65167 .26948 Mdot .652 .3486 Mdot .65233 .26952 Mdot .65267 .34856 Mdot .653 .26956 Mdot .65333 .34852 Mdot .65367 .2696 Mdot .654 .34848 Mdot .65433 .26964 Mdot .65467 .34844 Mdot .655 .26968 Mdot .65533 .3484 Mdot .65567 .26972 Mdot .656 .34836 Mdot .65633 .26976 Mdot .65667 .34832 Mdot .657 .2698 Mdot .65733 .34828 Mdot .65767 .26984 Mdot .658 .34824 Mdot .65833 .26988 Mdot .65867 .3482 Mdot .659 .26992 Mdot .65933 .34816 Mdot .65967 .26996 Mdot .66 .34813 Mdot .66033 .27 Mdot .66067 .34809 Mdot .661 .27004 Mdot .66133 .34805 Mdot .66167 .27008 Mdot .662 .34801 Mdot .66233 .27012 Mdot .66267 .34797 Mdot .663 .27016 Mdot .66333 .34793 Mdot .66367 .27019 Mdot .664 .34789 Mdot .66433 .27023 Mdot .66467 .34785 Mdot .665 .27027 Mdot .66533 .34781 Mdot .66567 .27031 Mdot .666 .34777 Mdot .66633 .27035 Mdot .66667 .34773 Mdot .667 .27039 Mdot .66733 .3477 Mdot .66767 .27043 Mdot .668 .34766 Mdot .66833 .27047 Mdot .66867 .34762 Mdot .669 .2705 Mdot .66933 .34758 Mdot .66967 .27054 Mdot .67 .34754 Mdot .67033 .27058 Mdot .67067 .3475 Mdot .671 .27062 Mdot .67133 .34747 Mdot .67167 .27066 Mdot .672 .34743 Mdot .67233 .2707 Mdot .67267 .34739 Mdot .673 .27073 Mdot .67333 .34735 Mdot .67367 .27077 Mdot .674 .34731 Mdot .67433 .27081 Mdot .67467 .34728 Mdot .675 .27085 Mdot .67533 .34724 Mdot .67567 .27088 Mdot .676 .3472 Mdot .67633 .27092 Mdot .67667 .34716 Mdot .677 .27096 Mdot .67733 .34713 Mdot .67767 .271 Mdot .678 .34709 Mdot .67833 .27103 Mdot .67867 .34705 Mdot .679 .27107 Mdot .67933 .34701 Mdot .67967 .27111 Mdot .68 .34698 Mdot .68033 .27115 Mdot .68067 .34694 Mdot .681 .27118 Mdot .68133 .3469 Mdot .68167 .27122 Mdot .682 .34686 Mdot .68233 .27126 Mdot .68267 .34683 Mdot .683 .27129 Mdot .68333 .34679 Mdot .68367 .27133 Mdot .684 .34675 Mdot .68433 .27137 Mdot .68467 .34672 Mdot .685 .2714 Mdot .68533 .34668 Mdot .68567 .27144 Mdot .686 .34664 Mdot .68633 .27148 Mdot .68667 .34661 Mdot .687 .27151 Mdot .68733 .34657 Mdot .68767 .27155 Mdot .688 .34653 Mdot .68833 .27159 Mdot .68867 .3465 Mdot .689 .27162 Mdot .68933 .34646 Mdot .68967 .27166 Mdot .69 .34643 Mdot .69033 .2717 Mdot .69067 .34639 Mdot .691 .27173 Mdot .69133 .34635 Mdot .69167 .27177 Mdot .692 .34632 Mdot .69233 .2718 Mdot .69267 .34628 Mdot .693 .27184 Mdot .69333 .34625 Mdot .69367 .27188 Mdot .694 .34621 Mdot .69433 .27191 Mdot .69467 .34618 Mdot .695 .27195 Mdot .69533 .34614 Mdot .69567 .27198 Mdot .696 .3461 Mdot .69633 .27202 Mdot .69667 .34607 Mdot .697 .27205 Mdot .69733 .34603 Mdot .69767 .27209 Mdot .698 .346 Mdot .69833 .27212 Mdot .69867 .34596 Mdot .699 .27216 Mdot .69933 .34593 Mdot .69967 .27219 Mdot .7 .34589 Mdot .70033 .27223 Mdot .70067 .34586 Mdot .701 .27226 Mdot .70133 .34582 Mdot .70167 .2723 Mdot .702 .34579 Mdot .70233 .27233 Mdot .70267 .34575 Mdot .703 .27237 Mdot .70333 .34572 Mdot .70367 .2724 Mdot .704 .34568 Mdot .70433 .27244 Mdot .70467 .34565 Mdot .705 .27247 Mdot .70533 .34561 Mdot .70567 .27251 Mdot .706 .34558 Mdot .70633 .27254 Mdot .70667 .34554 Mdot .707 .27258 Mdot .70733 .34551 Mdot .70767 .27261 Mdot .708 .34548 Mdot .70833 .27265 Mdot .70867 .34544 Mdot .709 .27268 Mdot .70933 .34541 Mdot .70967 .27271 Mdot .71 .34537 Mdot .71033 .27275 Mdot .71067 .34534 Mdot .711 .27278 Mdot .71133 .34531 Mdot .71167 .27282 Mdot .712 .34527 Mdot .71233 .27285 Mdot .71267 .34524 Mdot .713 .27288 Mdot .71333 .3452 Mdot .71367 .27292 Mdot .714 .34517 Mdot .71433 .27295 Mdot .71467 .34514 Mdot .715 .27298 Mdot .71533 .3451 Mdot .71567 .27302 Mdot .716 .34507 Mdot .71633 .27305 Mdot .71667 .34504 Mdot .717 .27309 Mdot .71733 .345 Mdot .71767 .27312 Mdot .718 .34497 Mdot .71833 .27315 Mdot .71867 .34494 Mdot .719 .27319 Mdot .71933 .3449 Mdot .71967 .27322 Mdot .72 .34487 Mdot .72033 .27325 Mdot .72067 .34484 Mdot .721 .27328 Mdot .72133 .3448 Mdot .72167 .27332 Mdot .722 .34477 Mdot .72233 .27335 Mdot .72267 .34474 Mdot .723 .27338 Mdot .72333 .3447 Mdot .72367 .27342 Mdot .724 .34467 Mdot .72433 .27345 Mdot .72467 .34464 Mdot .725 .27348 Mdot .72533 .34461 Mdot .72567 .27351 Mdot .726 .34457 Mdot .72633 .27355 Mdot .72667 .34454 Mdot .727 .27358 Mdot .72733 .34451 Mdot .72767 .27361 Mdot .728 .34448 Mdot .72833 .27364 Mdot .72867 .34444 Mdot .729 .27368 Mdot .72933 .34441 Mdot .72967 .27371 Mdot .73 .34438 Mdot .73033 .27374 Mdot .73067 .34435 Mdot .731 .27377 Mdot .73133 .34431 Mdot .73167 .27381 Mdot .732 .34428 Mdot .73233 .27384 Mdot .73267 .34425 Mdot .733 .27387 Mdot .73333 .34422 Mdot .73367 .2739 Mdot .734 .34419 Mdot .73433 .27393 Mdot .73467 .34415 Mdot .735 .27397 Mdot .73533 .34412 Mdot .73567 .274 Mdot .736 .34409 Mdot .73633 .27403 Mdot .73667 .34406 Mdot .737 .27406 Mdot .73733 .34403 Mdot .73767 .27409 Mdot .738 .344 Mdot .73833 .27412 Mdot .73867 .34396 Mdot .739 .27416 Mdot .73933 .34393 Mdot .73967 .27419 Mdot .74 .3439 Mdot .74033 .27422 Mdot .74067 .34387 Mdot .741 .27425 Mdot .74133 .34384 Mdot .74167 .27428 Mdot .742 .34381 Mdot .74233 .27431 Mdot .74267 .34378 Mdot .743 .27434 Mdot .74333 .34374 Mdot .74367 .27437 Mdot .744 .34371 Mdot .74433 .27441 Mdot .74467 .34368 Mdot .745 .27444 Mdot .74533 .34365 Mdot .74567 .27447 Mdot .746 .34362 Mdot .74633 .2745 Mdot .74667 .34359 Mdot .747 .27453 Mdot .74733 .34356 Mdot .74767 .27456 Mdot .748 .34353 Mdot .74833 .27459 Mdot .74867 .3435 Mdot .749 .27462 Mdot .74933 .34347 Mdot .74967 .27465 Mdot .75 .34344 Mdot .75033 .27468 Mdot .75067 .34341 Mdot .751 .27471 Mdot .75133 .34338 Mdot .75167 .27474 Mdot .752 .34334 Mdot .75233 .27477 Mdot .75267 .34331 Mdot .753 .2748 Mdot .75333 .34328 Mdot .75367 .27483 Mdot .754 .34325 Mdot .75433 .27487 Mdot .75467 .34322 Mdot .755 .2749 Mdot .75533 .34319 Mdot .75567 .27493 Mdot .756 .34316 Mdot .75633 .27496 Mdot .75667 .34313 Mdot .757 .27499 Mdot .75733 .3431 Mdot .75767 .27502 Mdot .758 .34307 Mdot .75833 .27505 Mdot .75867 .34304 Mdot .759 .27508 Mdot .75933 .34301 Mdot .75967 .27511 Mdot .76 .34298 Mdot .76033 .27514 Mdot .76067 .34295 Mdot .761 .27516 Mdot .76133 .34292 Mdot .76167 .27519 Mdot .762 .34289 Mdot .76233 .27522 Mdot .76267 .34287 Mdot .763 .27525 Mdot .76333 .34284 Mdot .76367 .27528 Mdot .764 .34281 Mdot .76433 .27531 Mdot .76467 .34278 Mdot .765 .27534 Mdot .76533 .34275 Mdot .76567 .27537 Mdot .766 .34272 Mdot .76633 .2754 Mdot .76667 .34269 Mdot .767 .27543 Mdot .76733 .34266 Mdot .76767 .27546 Mdot .768 .34263 Mdot .76833 .27549 Mdot .76867 .3426 Mdot .769 .27552 Mdot .76933 .34257 Mdot .76967 .27555 Mdot .77 .34254 Mdot .77033 .27558 Mdot .77067 .34251 Mdot .771 .2756 Mdot .77133 .34249 Mdot .77167 .27563 Mdot .772 .34246 Mdot .77233 .27566 Mdot .77267 .34243 Mdot .773 .27569 Mdot .77333 .3424 Mdot .77367 .27572 Mdot .774 .34237 Mdot .77433 .27575 Mdot .77467 .34234 Mdot .775 .27578 Mdot .77533 .34231 Mdot .77567 .27581 Mdot .776 .34228 Mdot .77633 .27583 Mdot .77667 .34226 Mdot .777 .27586 Mdot .77733 .34223 Mdot .77767 .27589 Mdot .778 .3422 Mdot .77833 .27592 Mdot .77867 .34217 Mdot .779 .27595 Mdot .77933 .34214 Mdot .77967 .27598 Mdot .78 .34211 Mdot .78033 .276 Mdot .78067 .34209 Mdot .781 .27603 Mdot .78133 .34206 Mdot .78167 .27606 Mdot .782 .34203 Mdot .78233 .27609 Mdot .78267 .342 Mdot .783 .27612 Mdot .78333 .34197 Mdot .78367 .27614 Mdot .784 .34195 Mdot .78433 .27617 Mdot .78467 .34192 Mdot .785 .2762 Mdot .78533 .34189 Mdot .78567 .27623 Mdot .786 .34186 Mdot .78633 .27626 Mdot .78667 .34183 Mdot .787 .27628 Mdot .78733 .34181 Mdot .78767 .27631 Mdot .788 .34178 Mdot .78833 .27634 Mdot .78867 .34175 Mdot .789 .27637 Mdot .78933 .34172 Mdot .78967 .27639 Mdot .79 .3417 Mdot .79033 .27642 Mdot .79067 .34167 Mdot .791 .27645 Mdot .79133 .34164 Mdot .79167 .27648 Mdot .792 .34161 Mdot .79233 .2765 Mdot .79267 .34159 Mdot .793 .27653 Mdot .79333 .34156 Mdot .79367 .27656 Mdot .794 .34153 Mdot .79433 .27659 Mdot .79467 .3415 Mdot .795 .27661 Mdot .79533 .34148 Mdot .79567 .27664 Mdot .796 .34145 Mdot .79633 .27667 Mdot .79667 .34142 Mdot .797 .2767 Mdot .79733 .3414 Mdot .79767 .27672 Mdot .798 .34137 Mdot .79833 .27675 Mdot .79867 .34134 Mdot .799 .27678 Mdot .79933 .34131 Mdot .79967 .2768 Mdot .8 .34129 Mdot .80033 .27683 Mdot .80067 .34126 Mdot .801 .27686 Mdot .80133 .34123 Mdot .80167 .27688 Mdot .802 .34121 Mdot .80233 .27691 Mdot .80267 .34118 Mdot .803 .27694 Mdot .80333 .34115 Mdot .80367 .27696 Mdot .804 .34113 Mdot .80433 .27699 Mdot .80467 .3411 Mdot .805 .27702 Mdot .80533 .34107 Mdot .80567 .27704 Mdot .806 .34105 Mdot .80633 .27707 Mdot .80667 .34102 Mdot .807 .2771 Mdot .80733 .34099 Mdot .80767 .27712 Mdot .808 .34097 Mdot .80833 .27715 Mdot .80867 .34094 Mdot .809 .27718 Mdot .80933 .34092 Mdot .80967 .2772 Mdot .81 .34089 Mdot .81033 .27723 Mdot .81067 .34086 Mdot .811 .27725 Mdot .81133 .34084 Mdot .81167 .27728 Mdot .812 .34081 Mdot .81233 .27731 Mdot .81267 .34078 Mdot .813 .27733 Mdot .81333 .34076 Mdot .81367 .27736 Mdot .814 .34073 Mdot .81433 .27738 Mdot .81467 .34071 Mdot .815 .27741 Mdot .81533 .34068 Mdot .81567 .27744 Mdot .816 .34066 Mdot .81633 .27746 Mdot .81667 .34063 Mdot .817 .27749 Mdot .81733 .3406 Mdot .81767 .27751 Mdot .818 .34058 Mdot .81833 .27754 Mdot .81867 .34055 Mdot .819 .27756 Mdot .81933 .34053 Mdot .81967 .27759 Mdot .82 .3405 Mdot .82033 .27762 Mdot .82067 .34048 Mdot .821 .27764 Mdot .82133 .34045 Mdot .82167 .27767 Mdot .822 .34042 Mdot .82233 .27769 Mdot .82267 .3404 Mdot .823 .27772 Mdot .82333 .34037 Mdot .82367 .27774 Mdot .824 .34035 Mdot .82433 .27777 Mdot .82467 .34032 Mdot .825 .27779 Mdot .82533 .3403 Mdot .82567 .27782 Mdot .826 .34027 Mdot 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.12371 Mdot .324 .20961 Mdot .32433 .1238 Mdot .32467 .20953 Mdot .325 .12389 Mdot .32533 .20944 Mdot .32567 .12398 Mdot .326 .20935 Mdot .32633 .12406 Mdot .32667 .20926 Mdot .327 .12415 Mdot .32733 .20918 Mdot .32767 .12424 Mdot .328 .20909 Mdot .32833 .12432 Mdot .32867 .209 Mdot .329 .12441 Mdot .32933 .20892 Mdot .32967 .1245 Mdot .33 .20883 Mdot .33033 .12458 Mdot .33067 .20875 Mdot .331 .12467 Mdot .33133 .20866 Mdot .33167 .12475 Mdot .332 .20858 Mdot .33233 .12483 Mdot .33267 .2085 Mdot .333 .12492 Mdot .33333 .20841 Mdot .33367 .125 Mdot .334 .20833 Mdot .33433 .12508 Mdot .33467 .20825 Mdot .335 .12517 Mdot .33533 .20816 Mdot .33567 .12525 Mdot .336 .20808 Mdot .33633 .12533 Mdot .33667 .208 Mdot .337 .12541 Mdot .33733 .20792 Mdot .33767 .12549 Mdot .338 .20784 Mdot .33833 .12558 Mdot .33867 .20775 Mdot .339 .12566 Mdot .33933 .20767 Mdot .33967 .12574 Mdot .34 .20759 Mdot .34033 .12582 Mdot .34067 .20751 Mdot .341 .1259 Mdot .34133 .20743 Mdot .34167 .12598 Mdot .342 .20735 Mdot .34233 .12606 Mdot .34267 .20728 Mdot .343 .12614 Mdot .34333 .2072 Mdot .34367 .12621 Mdot .344 .20712 Mdot .34433 .12629 Mdot .34467 .20704 Mdot .345 .12637 Mdot .34533 .20696 Mdot .34567 .12645 Mdot .346 .20688 Mdot .34633 .12653 Mdot .34667 .20681 Mdot .347 .1266 Mdot .34733 .20673 Mdot .34767 .12668 Mdot .348 .20665 Mdot .34833 .12676 Mdot .34867 .20658 Mdot .349 .12683 Mdot .34933 .2065 Mdot .34967 .12691 Mdot .35 .20642 Mdot .35033 .12698 Mdot .35067 .20635 Mdot .351 .12706 Mdot .35133 .20627 Mdot .35167 .12713 Mdot .352 .2062 Mdot .35233 .12721 Mdot .35267 .20612 Mdot .353 .12728 Mdot .35333 .20605 Mdot .35367 .12736 Mdot .354 .20598 Mdot .35433 .12743 Mdot .35467 .2059 Mdot .355 .12751 Mdot .35533 .20583 Mdot .35567 .12758 Mdot .356 .20575 Mdot .35633 .12765 Mdot .35667 .20568 Mdot .357 .12773 Mdot .35733 .20561 Mdot .35767 .1278 Mdot .358 .20554 Mdot .35833 .12787 Mdot .35867 .20546 Mdot .359 .12794 Mdot .35933 .20539 Mdot .35967 .12801 Mdot .36 .20532 Mdot .36033 .12809 Mdot .36067 .20525 Mdot .361 .12816 Mdot .36133 .20518 Mdot .36167 .12823 Mdot .362 .20511 Mdot .36233 .1283 Mdot .36267 .20504 Mdot .363 .12837 Mdot .36333 .20497 Mdot .36367 .12844 Mdot .364 .2049 Mdot .36433 .12851 Mdot .36467 .20483 Mdot .365 .12858 Mdot .36533 .20476 Mdot .36567 .12865 Mdot .366 .20469 Mdot .36633 .12872 Mdot .36667 .20462 Mdot .367 .12879 Mdot .36733 .20455 Mdot .36767 .12886 Mdot .368 .20448 Mdot .36833 .12892 Mdot .36867 .20441 Mdot .369 .12899 Mdot .36933 .20434 Mdot .36967 .12906 Mdot .37 .20428 Mdot .37033 .12913 Mdot .37067 .20421 Mdot .371 .1292 Mdot .37133 .20414 Mdot .37167 .12926 Mdot .372 .20407 Mdot .37233 .12933 Mdot .37267 .20401 Mdot .373 .1294 Mdot .37333 .20394 Mdot .37367 .12946 Mdot .374 .20387 Mdot .37433 .12953 Mdot .37467 .20381 Mdot .375 .1296 Mdot .37533 .20374 Mdot .37567 .12966 Mdot .376 .20368 Mdot .37633 .12973 Mdot .37667 .20361 Mdot .377 .12979 Mdot .37733 .20355 Mdot .37767 .12986 Mdot .378 .20348 Mdot .37833 .12992 Mdot .37867 .20342 Mdot .379 .12999 Mdot .37933 .20335 Mdot .37967 .13005 Mdot .38 .20329 Mdot .38033 .13012 Mdot .38067 .20322 Mdot .381 .13018 Mdot .38133 .20316 Mdot .38167 .13024 Mdot .382 .2031 Mdot .38233 .13031 Mdot .38267 .20303 Mdot .383 .13037 Mdot .38333 .20297 Mdot .38367 .13043 Mdot .384 .20291 Mdot .38433 .1305 Mdot .38467 .20284 Mdot .385 .13056 Mdot .38533 .20278 Mdot .38567 .13062 Mdot .386 .20272 Mdot .38633 .13068 Mdot .38667 .20266 Mdot .387 .13075 Mdot .38733 .20259 Mdot .38767 .13081 Mdot .388 .20253 Mdot .38833 .13087 Mdot .38867 .20247 Mdot .389 .13093 Mdot .38933 .20241 Mdot .38967 .13099 Mdot .39 .20235 Mdot .39033 .13105 Mdot .39067 .20229 Mdot .391 .13111 Mdot .39133 .20223 Mdot .39167 .13117 Mdot .392 .20217 Mdot .39233 .13123 Mdot .39267 .20211 Mdot .393 .13129 Mdot .39333 .20205 Mdot .39367 .13135 Mdot .394 .20199 Mdot .39433 .13141 Mdot .39467 .20193 Mdot .395 .13147 Mdot .39533 .20187 Mdot .39567 .13153 Mdot .396 .20181 Mdot .39633 .13159 Mdot .39667 .20175 Mdot .397 .13165 Mdot .39733 .20169 Mdot .39767 .13171 Mdot .398 .20163 Mdot .39833 .13177 Mdot .39867 .20157 Mdot .399 .13183 Mdot .39933 .20152 Mdot .39967 .13188 Mdot .4 .20146 Mdot .40033 .13194 Mdot .40067 .2014 Mdot .401 .132 Mdot .40133 .20134 Mdot .40167 .13206 Mdot .402 .20128 Mdot .40233 .13212 Mdot .40267 .20123 Mdot .403 .13217 Mdot .40333 .20117 Mdot .40367 .13223 Mdot .404 .20111 Mdot .40433 .13229 Mdot .40467 .20106 Mdot .405 .13234 Mdot .40533 .201 Mdot .40567 .1324 Mdot .406 .20094 Mdot .40633 .13246 Mdot .40667 .20089 Mdot .407 .13251 Mdot .40733 .20083 Mdot .40767 .13257 Mdot .408 .20078 Mdot .40833 .13262 Mdot .40867 .20072 Mdot .409 .13268 Mdot .40933 .20066 Mdot .40967 .13273 Mdot .41 .20061 Mdot .41033 .13279 Mdot .41067 .20055 Mdot .411 .13284 Mdot .41133 .2005 Mdot .41167 .1329 Mdot .412 .20044 Mdot .41233 .13295 Mdot .41267 .20039 Mdot .413 .13301 Mdot .41333 .20034 Mdot .41367 .13306 Mdot .414 .20028 Mdot .41433 .13312 Mdot .41467 .20023 Mdot .415 .13317 Mdot .41533 .20017 Mdot .41567 .13322 Mdot .416 .20012 Mdot .41633 .13328 Mdot .41667 .20007 Mdot .417 .13333 Mdot .41733 .20001 Mdot .41767 .13338 Mdot .418 .19996 Mdot .41833 .13344 Mdot .41867 .19991 Mdot .419 .13349 Mdot .41933 .19985 Mdot .41967 .13354 Mdot .42 .1998 Mdot .42033 .1336 Mdot .42067 .19975 Mdot .421 .13365 Mdot .42133 .1997 Mdot .42167 .1337 Mdot .422 .19964 Mdot .42233 .13375 Mdot .42267 .19959 Mdot .423 .1338 Mdot .42333 .19954 Mdot .42367 .13386 Mdot .424 .19949 Mdot .42433 .13391 Mdot .42467 .19944 Mdot .425 .13396 Mdot .42533 .19939 Mdot .42567 .13401 Mdot .426 .19934 Mdot .42633 .13406 Mdot .42667 .19928 Mdot .427 .13411 Mdot .42733 .19923 Mdot .42767 .13416 Mdot .428 .19918 Mdot .42833 .13421 Mdot .42867 .19913 Mdot .429 .13426 Mdot .42933 .19908 Mdot .42967 .13431 Mdot .43 .19903 Mdot .43033 .13436 Mdot .43067 .19898 Mdot .431 .13441 Mdot .43133 .19893 Mdot .43167 .13446 Mdot .432 .19888 Mdot .43233 .13451 Mdot .43267 .19883 Mdot .433 .13456 Mdot .43333 .19878 Mdot .43367 .13461 Mdot .434 .19873 Mdot .43433 .13466 Mdot .43467 .19868 Mdot .435 .13471 Mdot .43533 .19864 Mdot .43567 .13476 Mdot .436 .19859 Mdot .43633 .13481 Mdot .43667 .19854 Mdot .437 .13486 Mdot .43733 .19849 Mdot .43767 .13491 Mdot .438 .19844 Mdot .43833 .13495 Mdot .43867 .19839 Mdot .439 .135 Mdot .43933 .19834 Mdot .43967 .13505 Mdot .44 .1983 Mdot .44033 .1351 Mdot .44067 .19825 Mdot .441 .13515 Mdot .44133 .1982 Mdot .44167 .13519 Mdot .442 .19815 Mdot .44233 .13524 Mdot .44267 .19811 Mdot .443 .13529 Mdot .44333 .19806 Mdot .44367 .13534 Mdot .444 .19801 Mdot .44433 .13538 Mdot .44467 .19796 Mdot .445 .13543 Mdot .44533 .19792 Mdot .44567 .13548 Mdot .446 .19787 Mdot .44633 .13552 Mdot .44667 .19782 Mdot .447 .13557 Mdot .44733 .19778 Mdot .44767 .13562 Mdot .448 .19773 Mdot .44833 .13566 Mdot .44867 .19769 Mdot .449 .13571 Mdot .44933 .19764 Mdot .44967 .13575 Mdot .45 .19759 Mdot .45033 .1358 Mdot .45067 .19755 Mdot .451 .13585 Mdot .45133 .1975 Mdot .45167 .13589 Mdot .452 .19746 Mdot .45233 .13594 Mdot .45267 .19741 Mdot .453 .13598 Mdot .45333 .19737 Mdot .45367 .13603 Mdot .454 .19732 Mdot .45433 .13607 Mdot .45467 .19728 Mdot .455 .13612 Mdot .45533 .19723 Mdot .45567 .13616 Mdot .456 .19719 Mdot .45633 .13621 Mdot .45667 .19714 Mdot .457 .13625 Mdot .45733 .1971 Mdot .45767 .1363 Mdot .458 .19705 Mdot .45833 .13634 Mdot .45867 .19701 Mdot .459 .13638 Mdot .45933 .19697 Mdot .45967 .13643 Mdot .46 .19692 Mdot .46033 .13647 Mdot .46067 .19688 Mdot .461 .13651 Mdot .46133 .19683 Mdot .46167 .13656 Mdot .462 .19679 Mdot .46233 .1366 Mdot .46267 .19675 Mdot .463 .13665 Mdot .46333 .1967 Mdot .46367 .13669 Mdot .464 .19666 Mdot .46433 .13673 Mdot .46467 .19662 Mdot .465 .13677 Mdot .46533 .19658 Mdot .46567 .13682 Mdot .466 .19653 Mdot .46633 .13686 Mdot .46667 .19649 Mdot .467 .1369 Mdot .46733 .19645 Mdot .46767 .13694 Mdot .468 .19641 Mdot .46833 .13699 Mdot .46867 .19636 Mdot .469 .13703 Mdot .46933 .19632 Mdot .46967 .13707 Mdot .47 .19628 Mdot .47033 .13711 Mdot .47067 .19624 Mdot .471 .13716 Mdot .47133 .19619 Mdot .47167 .1372 Mdot .472 .19615 Mdot .47233 .13724 Mdot .47267 .19611 Mdot .473 .13728 Mdot .47333 .19607 Mdot .47367 .13732 Mdot .474 .19603 Mdot .47433 .13736 Mdot .47467 .19599 Mdot .475 .1374 Mdot .47533 .19595 Mdot .47567 .13745 Mdot .476 .19591 Mdot .47633 .13749 Mdot .47667 .19586 Mdot .477 .13753 Mdot .47733 .19582 Mdot .47767 .13757 Mdot .478 .19578 Mdot .47833 .13761 Mdot .47867 .19574 Mdot .479 .13765 Mdot .47933 .1957 Mdot .47967 .13769 Mdot .48 .19566 Mdot .48033 .13773 Mdot .48067 .19562 Mdot .481 .13777 Mdot .48133 .19558 Mdot .48167 .13781 Mdot .482 .19554 Mdot .48233 .13785 Mdot .48267 .1955 Mdot .483 .13789 Mdot .48333 .19546 Mdot .48367 .13793 Mdot .484 .19542 Mdot .48433 .13797 Mdot .48467 .19538 Mdot .485 .13801 Mdot .48533 .19534 Mdot .48567 .13805 Mdot .486 .1953 Mdot .48633 .13809 Mdot .48667 .19527 Mdot .487 .13813 Mdot .48733 .19523 Mdot .48767 .13816 Mdot .488 .19519 Mdot .48833 .1382 Mdot .48867 .19515 Mdot .489 .13824 Mdot .48933 .19511 Mdot .48967 .13828 Mdot .49 .19507 Mdot .49033 .13832 Mdot .49067 .19503 Mdot .491 .13836 Mdot .49133 .19499 Mdot .49167 .1384 Mdot .492 .19496 Mdot .49233 .13843 Mdot .49267 .19492 Mdot .493 .13847 Mdot .49333 .19488 Mdot .49367 .13851 Mdot .494 .19484 Mdot .49433 .13855 Mdot .49467 .1948 Mdot .495 .13859 Mdot .49533 .19477 Mdot .49567 .13862 Mdot .496 .19473 Mdot .49633 .13866 Mdot .49667 .19469 Mdot .497 .1387 Mdot .49733 .19465 Mdot .49767 .13874 Mdot .498 .19461 Mdot .49833 .13878 Mdot .49867 .19458 Mdot .499 .13881 Mdot .49933 .19454 Mdot .49967 .13885 Mdot .5 .1945 Mdot .50033 .13889 Mdot .50067 .19447 Mdot .501 .13892 Mdot .50133 .19443 Mdot .50167 .13896 Mdot .502 .19439 Mdot .50233 .139 Mdot .50267 .19436 Mdot .503 .13903 Mdot .50333 .19432 Mdot .50367 .13907 Mdot .504 .19428 Mdot .50433 .13911 Mdot .50467 .19425 Mdot .505 .13914 Mdot .50533 .19421 Mdot .50567 .13918 Mdot .506 .19417 Mdot .50633 .13922 Mdot .50667 .19414 Mdot .507 .13925 Mdot .50733 .1941 Mdot .50767 .13929 Mdot .508 .19406 Mdot .50833 .13932 Mdot .50867 .19403 Mdot .509 .13936 Mdot .50933 .19399 Mdot .50967 .1394 Mdot .51 .19396 Mdot .51033 .13943 Mdot .51067 .19392 Mdot .511 .13947 Mdot .51133 .19389 Mdot .51167 .1395 Mdot .512 .19385 Mdot .51233 .13954 Mdot .51267 .19382 Mdot .513 .13957 Mdot .51333 .19378 Mdot .51367 .13961 Mdot .514 .19375 Mdot .51433 .13964 Mdot .51467 .19371 Mdot .515 .13968 Mdot .51533 .19368 Mdot .51567 .13971 Mdot .516 .19364 Mdot .51633 .13975 Mdot .51667 .19361 Mdot .517 .13978 Mdot .51733 .19357 Mdot .51767 .13982 Mdot .518 .19354 Mdot .51833 .13985 Mdot .51867 .1935 Mdot .519 .13989 Mdot .51933 .19347 Mdot .51967 .13992 Mdot .52 .19343 Mdot .52033 .13996 Mdot .52067 .1934 Mdot .521 .13999 Mdot .52133 .19336 Mdot .52167 .14002 Mdot .522 .19333 Mdot .52233 .14006 Mdot .52267 .1933 Mdot .523 .14009 Mdot .52333 .19326 Mdot .52367 .14013 Mdot .524 .19323 Mdot .52433 .14016 Mdot .52467 .1932 Mdot .525 .14019 Mdot .52533 .19316 Mdot .52567 .14023 Mdot .526 .19313 Mdot .52633 .14026 Mdot .52667 .19309 Mdot .527 .14029 Mdot .52733 .19306 Mdot .52767 .14033 Mdot .528 .19303 Mdot .52833 .14036 Mdot .52867 .19299 Mdot .529 .14039 Mdot .52933 .19296 Mdot .52967 .14043 Mdot .53 .19293 Mdot .53033 .14046 Mdot .53067 .1929 Mdot .531 .14049 Mdot .53133 .19286 Mdot .53167 .14052 Mdot .532 .19283 Mdot .53233 .14056 Mdot .53267 .1928 Mdot .533 .14059 Mdot .53333 .19276 Mdot .53367 .14062 Mdot .534 .19273 Mdot .53433 .14066 Mdot .53467 .1927 Mdot .535 .14069 Mdot .53533 .19267 Mdot .53567 .14072 Mdot .536 .19263 Mdot .53633 .14075 Mdot .53667 .1926 Mdot .537 .14078 Mdot .53733 .19257 Mdot .53767 .14082 Mdot .538 .19254 Mdot .53833 .14085 Mdot .53867 .19251 Mdot .539 .14088 Mdot .53933 .19247 Mdot .53967 .14091 Mdot .54 .19244 Mdot .54033 .14094 Mdot .54067 .19241 Mdot .541 .14098 Mdot .54133 .19238 Mdot .54167 .14101 Mdot .542 .19235 Mdot .54233 .14104 Mdot .54267 .19232 Mdot .543 .14107 Mdot .54333 .19228 Mdot .54367 .1411 Mdot .544 .19225 Mdot .54433 .14113 Mdot .54467 .19222 Mdot .545 .14116 Mdot .54533 .19219 Mdot .54567 .1412 Mdot .546 .19216 Mdot .54633 .14123 Mdot .54667 .19213 Mdot .547 .14126 Mdot .54733 .1921 Mdot .54767 .14129 Mdot .548 .19207 Mdot .54833 .14132 Mdot .54867 .19204 Mdot .549 .14135 Mdot .54933 .192 Mdot .54967 .14138 Mdot .55 .19197 Mdot .55033 .14141 Mdot .55067 .19194 Mdot .551 .14144 Mdot .55133 .19191 Mdot .55167 .14147 Mdot .552 .19188 Mdot .55233 .1415 Mdot .55267 .19185 Mdot .553 .14153 Mdot .55333 .19182 Mdot .55367 .14156 Mdot .554 .19179 Mdot .55433 .14159 Mdot .55467 .19176 Mdot .555 .14162 Mdot .55533 .19173 Mdot .55567 .14165 Mdot .556 .1917 Mdot .55633 .14168 Mdot .55667 .19167 Mdot .557 .14171 Mdot .55733 .19164 Mdot .55767 .14174 Mdot .558 .19161 Mdot .55833 .14177 Mdot .55867 .19158 Mdot .559 .1418 Mdot .55933 .19155 Mdot .55967 .14183 Mdot .56 .19152 Mdot .56033 .14186 Mdot .56067 .19149 Mdot .561 .14189 Mdot .56133 .19146 Mdot .56167 .14192 Mdot .562 .19143 Mdot .56233 .14195 Mdot .56267 .1914 Mdot .563 .14198 Mdot .56333 .19138 Mdot .56367 .14201 Mdot .564 .19135 Mdot .56433 .14204 Mdot .56467 .19132 Mdot .565 .14207 Mdot .56533 .19129 Mdot .56567 .1421 Mdot .566 .19126 Mdot .56633 .14213 Mdot .56667 .19123 Mdot .567 .14216 Mdot .56733 .1912 Mdot .56767 .14218 Mdot .568 .19117 Mdot .56833 .14221 Mdot .56867 .19114 Mdot .569 .14224 Mdot .56933 .19112 Mdot .56967 .14227 Mdot .57 .19109 Mdot .57033 .1423 Mdot .57067 .19106 Mdot .571 .14233 Mdot .57133 .19103 Mdot .57167 .14236 Mdot .572 .191 Mdot .57233 .14238 Mdot .57267 .19097 Mdot .573 .14241 Mdot .57333 .19094 Mdot .57367 .14244 Mdot .574 .19092 Mdot .57433 .14247 Mdot .57467 .19089 Mdot .575 .1425 Mdot .57533 .19086 Mdot .57567 .14252 Mdot .576 .19083 Mdot .57633 .14255 Mdot .57667 .1908 Mdot .577 .14258 Mdot .57733 .19078 Mdot .57767 .14261 Mdot .578 .19075 Mdot .57833 .14264 Mdot .57867 .19072 Mdot .579 .14266 Mdot .57933 .19069 Mdot .57967 .14269 Mdot .58 .19067 Mdot .58033 .14272 Mdot .58067 .19064 Mdot .581 .14275 Mdot .58133 .19061 Mdot .58167 .14277 Mdot .582 .19058 Mdot .58233 .1428 Mdot .58267 .19056 Mdot .583 .14283 Mdot .58333 .19053 Mdot .58367 .14286 Mdot .584 .1905 Mdot .58433 .14288 Mdot .58467 .19047 Mdot .585 .14291 Mdot .58533 .19045 Mdot .58567 .14294 Mdot .586 .19042 Mdot .58633 .14296 Mdot .58667 .19039 Mdot .587 .14299 Mdot .58733 .19037 Mdot .58767 .14302 Mdot .588 .19034 Mdot .58833 .14304 Mdot .58867 .19031 Mdot .589 .14307 Mdot .58933 .19029 Mdot .58967 .1431 Mdot .59 .19026 Mdot .59033 .14312 Mdot .59067 .19023 Mdot .591 .14315 Mdot .59133 .19021 Mdot .59167 .14318 Mdot .592 .19018 Mdot .59233 .1432 Mdot .59267 .19015 Mdot .593 .14323 Mdot .59333 .19013 Mdot .59367 .14326 Mdot .594 .1901 Mdot .59433 .14328 Mdot .59467 .19007 Mdot .595 .14331 Mdot .59533 .19005 Mdot .59567 .14334 Mdot .596 .19002 Mdot .59633 .14336 Mdot .59667 .19 Mdot .597 .14339 Mdot .59733 .18997 Mdot .59767 .14341 Mdot .598 .18994 Mdot .59833 .14344 Mdot .59867 .18992 Mdot .599 .14347 Mdot .59933 .18989 Mdot .59967 .14349 Mdot .6 .18987 Mdot .60033 .14352 Mdot .60067 .18984 Mdot .601 .14354 Mdot .60133 .18982 Mdot .60167 .14357 Mdot .602 .18979 Mdot .60233 .14359 Mdot .60267 .18976 Mdot .603 .14362 Mdot .60333 .18974 Mdot .60367 .14365 Mdot .604 .18971 Mdot .60433 .14367 Mdot .60467 .18969 Mdot .605 .1437 Mdot .60533 .18966 Mdot .60567 .14372 Mdot .606 .18964 Mdot .60633 .14375 Mdot .60667 .18961 Mdot .607 .14377 Mdot .60733 .18959 Mdot .60767 .1438 Mdot .608 .18956 Mdot .60833 .14382 Mdot .60867 .18954 Mdot .609 .14385 Mdot .60933 .18951 Mdot .60967 .14387 Mdot .61 .18949 Mdot .61033 .1439 Mdot .61067 .18946 Mdot .611 .14392 Mdot .61133 .18944 Mdot .61167 .14395 Mdot .612 .18941 Mdot .61233 .14397 Mdot .61267 .18939 Mdot .613 .144 Mdot .61333 .18936 Mdot .61367 .14402 Mdot .614 .18934 Mdot .61433 .14405 Mdot .61467 .18931 Mdot .615 .14407 Mdot .61533 .18929 Mdot .61567 .14409 Mdot .616 .18926 Mdot .61633 .14412 Mdot .61667 .18924 Mdot .617 .14414 Mdot .61733 .18922 Mdot .61767 .14417 Mdot .618 .18919 Mdot .61833 .14419 Mdot .61867 .18917 Mdot .619 .14422 Mdot .61933 .18914 Mdot .61967 .14424 Mdot .62 .18912 Mdot .62033 .14426 Mdot .62067 .18909 Mdot .621 .14429 Mdot .62133 .18907 Mdot .62167 .14431 Mdot .622 .18905 Mdot .62233 .14434 Mdot .62267 .18902 Mdot .623 .14436 Mdot .62333 .189 Mdot .62367 .14438 Mdot .624 .18898 Mdot .62433 .14441 Mdot .62467 .18895 Mdot .625 .14443 Mdot .62533 .18893 Mdot .62567 .14446 Mdot .626 .1889 Mdot .62633 .14448 Mdot .62667 .18888 Mdot .627 .1445 Mdot .62733 .18886 Mdot .62767 .14453 Mdot .628 .18883 Mdot .62833 .14455 Mdot .62867 .18881 Mdot .629 .14457 Mdot .62933 .18879 Mdot .62967 .1446 Mdot .63 .18876 Mdot .63033 .14462 Mdot .63067 .18874 Mdot .631 .14464 Mdot .63133 .18872 Mdot .63167 .14467 Mdot .632 .18869 Mdot .63233 .14469 Mdot .63267 .18867 Mdot .633 .14471 Mdot .63333 .18865 Mdot .63367 .14474 Mdot .634 .18862 Mdot .63433 .14476 Mdot .63467 .1886 Mdot .635 .14478 Mdot .63533 .18858 Mdot .63567 .14481 Mdot .636 .18855 Mdot .63633 .14483 Mdot .63667 .18853 Mdot .637 .14485 Mdot .63733 .18851 Mdot .63767 .14487 Mdot .638 .18849 Mdot .63833 .1449 Mdot .63867 .18846 Mdot .639 .14492 Mdot .63933 .18844 Mdot .63967 .14494 Mdot .64 .18842 Mdot .64033 .14496 Mdot .64067 .1884 Mdot .641 .14499 Mdot .64133 .18837 Mdot .64167 .14501 Mdot .642 .18835 Mdot .64233 .14503 Mdot .64267 .18833 Mdot .643 .14505 Mdot .64333 .18831 Mdot .64367 .14508 Mdot .644 .18828 Mdot .64433 .1451 Mdot .64467 .18826 Mdot .645 .14512 Mdot .64533 .18824 Mdot .64567 .14514 Mdot .646 .18822 Mdot .64633 .14517 Mdot .64667 .18819 Mdot .647 .14519 Mdot .64733 .18817 Mdot .64767 .14521 Mdot .648 .18815 Mdot .64833 .14523 Mdot .64867 .18813 Mdot .649 .14525 Mdot .64933 .18811 Mdot .64967 .14528 Mdot .65 .18808 Mdot .65033 .1453 Mdot .65067 .18806 Mdot .651 .14532 Mdot .65133 .18804 Mdot .65167 .14534 Mdot .652 .18802 Mdot .65233 .14536 Mdot .65267 .188 Mdot .653 .14539 Mdot .65333 .18797 Mdot .65367 .14541 Mdot .654 .18795 Mdot .65433 .14543 Mdot .65467 .18793 Mdot .655 .14545 Mdot .65533 .18791 Mdot .65567 .14547 Mdot .656 .18789 Mdot .65633 .14549 Mdot .65667 .18787 Mdot .657 .14552 Mdot .65733 .18784 Mdot .65767 .14554 Mdot .658 .18782 Mdot .65833 .14556 Mdot .65867 .1878 Mdot .659 .14558 Mdot .65933 .18778 Mdot .65967 .1456 Mdot .66 .18776 Mdot .66033 .14562 Mdot .66067 .18774 Mdot .661 .14564 Mdot .66133 .18772 Mdot .66167 .14566 Mdot .662 .1877 Mdot .66233 .14569 Mdot .66267 .18767 Mdot .663 .14571 Mdot .66333 .18765 Mdot .66367 .14573 Mdot .664 .18763 Mdot .66433 .14575 Mdot .66467 .18761 Mdot .665 .14577 Mdot .66533 .18759 Mdot .66567 .14579 Mdot .666 .18757 Mdot .66633 .14581 Mdot .66667 .18755 Mdot .667 .14583 Mdot .66733 .18753 Mdot .66767 .14585 Mdot .668 .18751 Mdot .66833 .14587 Mdot .66867 .18749 Mdot .669 .1459 Mdot .66933 .18747 Mdot .66967 .14592 Mdot .67 .18744 Mdot .67033 .14594 Mdot .67067 .18742 Mdot .671 .14596 Mdot .67133 .1874 Mdot .67167 .14598 Mdot .672 .18738 Mdot .67233 .146 Mdot .67267 .18736 Mdot .673 .14602 Mdot .67333 .18734 Mdot .67367 .14604 Mdot .674 .18732 Mdot .67433 .14606 Mdot .67467 .1873 Mdot .675 .14608 Mdot .67533 .18728 Mdot .67567 .1461 Mdot .676 .18726 Mdot .67633 .14612 Mdot .67667 .18724 Mdot .677 .14614 Mdot .67733 .18722 Mdot .67767 .14616 Mdot .678 .1872 Mdot .67833 .14618 Mdot .67867 .18718 Mdot .679 .1462 Mdot .67933 .18716 Mdot .67967 .14622 Mdot .68 .18714 Mdot .68033 .14624 Mdot .68067 .18712 Mdot .681 .14626 Mdot .68133 .1871 Mdot .68167 .14628 Mdot .682 .18708 Mdot .68233 .1463 Mdot .68267 .18706 Mdot .683 .14632 Mdot .68333 .18704 Mdot .68367 .14634 Mdot .684 .18702 Mdot .68433 .14636 Mdot .68467 .187 Mdot .685 .14638 Mdot .68533 .18698 Mdot .68567 .1464 Mdot .686 .18696 Mdot .68633 .14642 Mdot .68667 .18694 Mdot .687 .14644 Mdot .68733 .18692 Mdot .68767 .14646 Mdot .688 .1869 Mdot .68833 .14648 Mdot .68867 .18688 Mdot .689 .1465 Mdot .68933 .18686 Mdot .68967 .14652 Mdot .69 .18684 Mdot .69033 .14654 Mdot .69067 .18682 Mdot .691 .14656 Mdot .69133 .1868 Mdot .69167 .14658 Mdot .692 .18678 Mdot .69233 .1466 Mdot .69267 .18677 Mdot .693 .14662 Mdot .69333 .18675 Mdot .69367 .14663 Mdot .694 .18673 Mdot .69433 .14665 Mdot .69467 .18671 Mdot .695 .14667 Mdot .69533 .18669 Mdot .69567 .14669 Mdot .696 .18667 Mdot .69633 .14671 Mdot .69667 .18665 Mdot .697 .14673 Mdot .69733 .18663 Mdot .69767 .14675 Mdot .698 .18661 Mdot .69833 .14677 Mdot .69867 .18659 Mdot .699 .14679 Mdot .69933 .18657 Mdot .69967 .14681 Mdot .7 .18656 Mdot .70033 .14683 Mdot .70067 .18654 Mdot .701 .14684 Mdot .70133 .18652 Mdot .70167 .14686 Mdot .702 .1865 Mdot .70233 .14688 Mdot .70267 .18648 Mdot .703 .1469 Mdot .70333 .18646 Mdot .70367 .14692 Mdot .704 .18644 Mdot .70433 .14694 Mdot .70467 .18642 Mdot .705 .14696 Mdot .70533 .1864 Mdot .70567 .14698 Mdot .706 .18639 Mdot .70633 .14699 Mdot .70667 .18637 Mdot .707 .14701 Mdot .70733 .18635 Mdot .70767 .14703 Mdot .708 .18633 Mdot .70833 .14705 Mdot .70867 .18631 Mdot .709 .14707 Mdot .70933 .18629 Mdot .70967 .14709 Mdot .71 .18628 Mdot .71033 .1471 Mdot .71067 .18626 Mdot .711 .14712 Mdot .71133 .18624 Mdot .71167 .14714 Mdot .712 .18622 Mdot .71233 .14716 Mdot .71267 .1862 Mdot .713 .14718 Mdot .71333 .18618 Mdot .71367 .1472 Mdot .714 .18617 Mdot .71433 .14721 Mdot .71467 .18615 Mdot .715 .14723 Mdot .71533 .18613 Mdot .71567 .14725 Mdot .716 .18611 Mdot .71633 .14727 Mdot .71667 .18609 Mdot .717 .14729 Mdot .71733 .18608 Mdot .71767 .14731 Mdot .718 .18606 Mdot .71833 .14732 Mdot .71867 .18604 Mdot .719 .14734 Mdot .71933 .18602 Mdot .71967 .14736 Mdot .72 .186 Mdot .72033 .14738 Mdot .72067 .18599 Mdot .721 .14739 Mdot .72133 .18597 Mdot .72167 .14741 Mdot .722 .18595 Mdot .72233 .14743 Mdot .72267 .18593 Mdot .723 .14745 Mdot .72333 .18591 Mdot .72367 .14747 Mdot .724 .1859 Mdot .72433 .14748 Mdot .72467 .18588 Mdot .725 .1475 Mdot .72533 .18586 Mdot .72567 .14752 Mdot .726 .18584 Mdot .72633 .14754 Mdot .72667 .18583 Mdot .727 .14755 Mdot .72733 .18581 Mdot .72767 .14757 Mdot .728 .18579 Mdot .72833 .14759 Mdot .72867 .18577 Mdot .729 .14761 Mdot .72933 .18576 Mdot .72967 .14762 Mdot .73 .18574 Mdot .73033 .14764 Mdot .73067 .18572 Mdot .731 .14766 Mdot .73133 .1857 Mdot .73167 .14768 Mdot .732 .18569 Mdot .73233 .14769 Mdot .73267 .18567 Mdot .733 .14771 Mdot .73333 .18565 Mdot .73367 .14773 Mdot .734 .18563 Mdot .73433 .14774 Mdot .73467 .18562 Mdot .735 .14776 Mdot .73533 .1856 Mdot .73567 .14778 Mdot .736 .18558 Mdot .73633 .1478 Mdot .73667 .18557 Mdot .737 .14781 Mdot .73733 .18555 Mdot .73767 .14783 Mdot .738 .18553 Mdot .73833 .14785 Mdot .73867 .18552 Mdot .739 .14786 Mdot .73933 .1855 Mdot .73967 .14788 Mdot .74 .18548 Mdot .74033 .1479 Mdot .74067 .18546 Mdot .741 .14792 Mdot .74133 .18545 Mdot .74167 .14793 Mdot .742 .18543 Mdot .74233 .14795 Mdot .74267 .18541 Mdot .743 .14797 Mdot .74333 .1854 Mdot .74367 .14798 Mdot .744 .18538 Mdot .74433 .148 Mdot .74467 .18536 Mdot .745 .14802 Mdot .74533 .18535 Mdot .74567 .14803 Mdot .746 .18533 Mdot .74633 .14805 Mdot .74667 .18531 Mdot .747 .14807 Mdot .74733 .1853 Mdot .74767 .14808 Mdot .748 .18528 Mdot .74833 .1481 Mdot .74867 .18526 Mdot .749 .14812 Mdot .74933 .18525 Mdot .74967 .14813 Mdot .75 .18523 Mdot .75033 .14815 Mdot .75067 .18521 Mdot .751 .14817 Mdot .75133 .1852 Mdot .75167 .14818 Mdot .752 .18518 Mdot .75233 .1482 Mdot .75267 .18516 Mdot .753 .14821 Mdot .75333 .18515 Mdot .75367 .14823 Mdot .754 .18513 Mdot .75433 .14825 Mdot .75467 .18512 Mdot .755 .14826 Mdot .75533 .1851 Mdot .75567 .14828 Mdot .756 .18508 Mdot .75633 .1483 Mdot .75667 .18507 Mdot .757 .14831 Mdot .75733 .18505 Mdot .75767 .14833 Mdot .758 .18503 Mdot .75833 .14834 Mdot .75867 .18502 Mdot .759 .14836 Mdot .75933 .185 Mdot .75967 .14838 Mdot .76 .18499 Mdot .76033 .14839 Mdot .76067 .18497 Mdot .761 .14841 Mdot .76133 .18495 Mdot .76167 .14842 Mdot .762 .18494 Mdot .76233 .14844 Mdot .76267 .18492 Mdot .763 .14846 Mdot .76333 .18491 Mdot .76367 .14847 Mdot .764 .18489 Mdot .76433 .14849 Mdot .76467 .18487 Mdot .765 .1485 Mdot .76533 .18486 Mdot .76567 .14852 Mdot .766 .18484 Mdot .76633 .14854 Mdot .76667 .18483 Mdot .767 .14855 Mdot .76733 .18481 Mdot .76767 .14857 Mdot .768 .1848 Mdot .76833 .14858 Mdot .76867 .18478 Mdot .769 .1486 Mdot .76933 .18476 Mdot .76967 .14861 Mdot .77 .18475 Mdot .77033 .14863 Mdot .77067 .18473 Mdot .771 .14865 Mdot .77133 .18472 Mdot .77167 .14866 Mdot .772 .1847 Mdot .77233 .14868 Mdot .77267 .18469 Mdot .773 .14869 Mdot .77333 .18467 Mdot .77367 .14871 Mdot .774 .18466 Mdot .77433 .14872 Mdot .77467 .18464 Mdot .775 .14874 Mdot .77533 .18462 Mdot .77567 .14875 Mdot .776 .18461 Mdot .77633 .14877 Mdot .77667 .18459 Mdot .777 .14878 Mdot .77733 .18458 Mdot .77767 .1488 Mdot .778 .18456 Mdot .77833 .14882 Mdot .77867 .18455 Mdot .779 .14883 Mdot .77933 .18453 Mdot .77967 .14885 Mdot .78 .18452 Mdot .78033 .14886 Mdot .78067 .1845 Mdot .781 .14888 Mdot .78133 .18449 Mdot .78167 .14889 Mdot .782 .18447 Mdot .78233 .14891 Mdot .78267 .18446 Mdot .783 .14892 Mdot .78333 .18444 Mdot .78367 .14894 Mdot .784 .18443 Mdot .78433 .14895 Mdot .78467 .18441 Mdot .785 .14897 Mdot .78533 .1844 Mdot .78567 .14898 Mdot .786 .18438 Mdot .78633 .149 Mdot .78667 .18437 Mdot .787 .14901 Mdot .78733 .18435 Mdot .78767 .14903 Mdot .788 .18434 Mdot .78833 .14904 Mdot .78867 .18432 Mdot .789 .14906 Mdot .78933 .18431 Mdot .78967 .14907 Mdot .79 .18429 Mdot .79033 .14909 Mdot .79067 .18428 Mdot .791 .1491 Mdot .79133 .18426 Mdot .79167 .14912 Mdot .792 .18425 Mdot .79233 .14913 Mdot .79267 .18423 Mdot .793 .14915 Mdot .79333 .18422 Mdot .79367 .14916 Mdot .794 .1842 Mdot .79433 .14918 Mdot .79467 .18419 Mdot .795 .14919 Mdot .79533 .18417 Mdot .79567 .1492 Mdot .796 .18416 Mdot .79633 .14922 Mdot .79667 .18414 Mdot .797 .14923 Mdot .79733 .18413 Mdot .79767 .14925 Mdot .798 .18412 Mdot .79833 .14926 Mdot .79867 .1841 Mdot .799 .14928 Mdot .79933 .18409 Mdot .79967 .14929 Mdot .8 .18407 Mdot .80033 .14931 Mdot .80067 .18406 Mdot .801 .14932 Mdot .80133 .18404 Mdot .80167 .14934 Mdot .802 .18403 Mdot .80233 .14935 Mdot .80267 .18401 Mdot .803 .14936 Mdot .80333 .184 Mdot .80367 .14938 Mdot .804 .18398 Mdot .80433 .14939 Mdot .80467 .18397 Mdot .805 .14941 Mdot .80533 .18396 Mdot .80567 .14942 Mdot .806 .18394 Mdot .80633 .14944 Mdot .80667 .18393 Mdot .807 .14945 Mdot .80733 .18391 Mdot .80767 .14946 Mdot .808 .1839 Mdot .80833 .14948 Mdot .80867 .18389 Mdot .809 .14949 Mdot .80933 .18387 Mdot .80967 .14951 Mdot .81 .18386 Mdot .81033 .14952 Mdot .81067 .18384 Mdot .811 .14954 Mdot .81133 .18383 Mdot .81167 .14955 Mdot .812 .18381 Mdot .81233 .14956 Mdot .81267 .1838 Mdot .813 .14958 Mdot .81333 .18379 Mdot .81367 .14959 Mdot .814 .18377 Mdot .81433 .14961 Mdot .81467 .18376 Mdot .815 .14962 Mdot .81533 .18374 Mdot .81567 .14963 Mdot .816 .18373 Mdot .81633 .14965 Mdot .81667 .18372 Mdot .817 .14966 Mdot .81733 .1837 Mdot .81767 .14968 Mdot .818 .18369 Mdot .81833 .14969 Mdot .81867 .18368 Mdot .819 .1497 Mdot .81933 .18366 Mdot .81967 .14972 Mdot .82 .18365 Mdot .82033 .14973 Mdot .82067 .18363 Mdot .821 .14974 Mdot .82133 .18362 Mdot .82167 .14976 Mdot .822 .18361 Mdot .82233 .14977 Mdot .82267 .18359 Mdot .823 .14979 Mdot .82333 .18358 Mdot .82367 .1498 Mdot .824 .18357 Mdot .82433 .14981 Mdot .82467 .18355 Mdot .825 .14983 Mdot .82533 .18354 Mdot .82567 .14984 Mdot .826 .18352 Mdot .82633 .14985 Mdot .82667 .18351 Mdot .827 .14987 Mdot .82733 .1835 Mdot .82767 .14988 Mdot .828 .18348 Mdot .82833 .14989 Mdot .82867 .18347 Mdot .829 .14991 Mdot .82933 .18346 Mdot .82967 .14992 Mdot .83 .18344 Mdot .83033 .14993 Mdot .83067 .18343 Mdot .831 .14995 Mdot .83133 .18342 Mdot .83167 .14996 Mdot .832 .1834 Mdot .83233 .14998 Mdot .83267 .18339 Mdot .833 .14999 Mdot .83333 .18338 Mdot .83367 .15 Mdot .834 .18336 Mdot .83433 .15002 Mdot .83467 .18335 Mdot .835 .15003 Mdot .83533 .18334 Mdot .83567 .15004 Mdot .836 .18332 Mdot .83633 .15005 Mdot .83667 .18331 Mdot .837 .15007 Mdot .83733 .1833 Mdot .83767 .15008 Mdot .838 .18328 Mdot .83833 .15009 Mdot .83867 .18327 Mdot .839 .15011 Mdot .83933 .18326 Mdot .83967 .15012 Mdot .84 .18324 Mdot .84033 .15013 Mdot .84067 .18323 Mdot .841 .15015 Mdot .84133 .18322 Mdot .84167 .15016 Mdot .842 .1832 Mdot .84233 .15017 Mdot .84267 .18319 Mdot .843 .15019 Mdot .84333 .18318 Mdot .84367 .1502 Mdot .844 .18317 Mdot .84433 .15021 Mdot .84467 .18315 Mdot .845 .15023 Mdot .84533 .18314 Mdot .84567 .15024 Mdot .846 .18313 Mdot .84633 .15025 Mdot .84667 .18311 Mdot .847 .15026 Mdot .84733 .1831 Mdot .84767 .15028 Mdot .848 .18309 Mdot .84833 .15029 Mdot .84867 .18307 Mdot .849 .1503 Mdot .84933 .18306 Mdot .84967 .15032 Mdot .85 .18305 Mdot .85033 .15033 Mdot .85067 .18304 Mdot .851 .15034 Mdot .85133 .18302 Mdot .85167 .15035 Mdot .852 .18301 Mdot .85233 .15037 Mdot .85267 .183 Mdot .853 .15038 Mdot .85333 .18298 Mdot .85367 .15039 Mdot .854 .18297 Mdot .85433 .15041 Mdot .85467 .18296 Mdot .855 .15042 Mdot .85533 .18295 Mdot .85567 .15043 Mdot .856 .18293 Mdot .85633 .15044 Mdot .85667 .18292 Mdot .857 .15046 Mdot .85733 .18291 Mdot .85767 .15047 Mdot .858 .1829 Mdot .85833 .15048 Mdot .85867 .18288 Mdot .859 .15049 Mdot .85933 .18287 Mdot .85967 .15051 Mdot .86 .18286 Mdot .86033 .15052 Mdot .86067 .18285 Mdot .861 .15053 Mdot .86133 .18283 Mdot .86167 .15054 Mdot .862 .18282 Mdot .86233 .15056 Mdot .86267 .18281 Mdot .863 .15057 Mdot .86333 .1828 Mdot .86367 .15058 Mdot .864 .18278 Mdot .86433 .15059 Mdot .86467 .18277 Mdot .865 .15061 Mdot .86533 .18276 Mdot .86567 .15062 Mdot .866 .18275 Mdot .86633 .15063 Mdot .86667 .18273 Mdot .867 .15064 Mdot .86733 .18272 Mdot .86767 .15066 Mdot .868 .18271 Mdot .86833 .15067 Mdot .86867 .1827 Mdot .869 .15068 Mdot .86933 .18268 Mdot .86967 .15069 Mdot .87 .18267 Mdot .87033 .1507 Mdot .87067 .18266 Mdot .871 .15072 Mdot .87133 .18265 Mdot .87167 .15073 Mdot .872 .18264 Mdot .87233 .15074 Mdot .87267 .18262 Mdot .873 .15075 Mdot .87333 .18261 Mdot .87367 .15077 Mdot .874 .1826 Mdot .87433 .15078 Mdot .87467 .18259 Mdot .875 .15079 Mdot .87533 .18258 Mdot .87567 .1508 Mdot .876 .18256 Mdot .87633 .15081 Mdot .87667 .18255 Mdot .877 .15083 Mdot .87733 .18254 Mdot .87767 .15084 Mdot .878 .18253 Mdot .87833 .15085 Mdot .87867 .18251 Mdot .879 .15086 Mdot .87933 .1825 Mdot .87967 .15087 Mdot .88 .18249 Mdot .88033 .15089 Mdot .88067 .18248 Mdot .881 .1509 Mdot .88133 .18247 Mdot .88167 .15091 Mdot .882 .18246 Mdot .88233 .15092 Mdot .88267 .18244 Mdot .883 .15093 Mdot .88333 .18243 Mdot .88367 .15095 Mdot .884 .18242 Mdot .88433 .15096 Mdot .88467 .18241 Mdot .885 .15097 Mdot .88533 .1824 Mdot .88567 .15098 Mdot .886 .18238 Mdot .88633 .15099 Mdot .88667 .18237 Mdot .887 .151 Mdot .88733 .18236 Mdot .88767 .15102 Mdot .888 .18235 Mdot .88833 .15103 Mdot .88867 .18234 Mdot .889 .15104 Mdot .88933 .18233 Mdot .88967 .15105 Mdot .89 .18231 Mdot .89033 .15106 Mdot .89067 .1823 Mdot .891 .15108 Mdot .89133 .18229 Mdot 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Andernfalls w\ \[ADoubleDot]re der \[CurlyEpsilon]\[Dash]Streifen \[UDoubleDot]berhaupt \ nicht mehr erkennbar! Auch die Ma\[SZ]st\[ADoubleDot]be sind unterschiedlich! Es hat bis in die Mitte des vorvorigen Jahrhunderts gedauert, bis diese \ anschauliche Vorstellung eine im heutigen Sinne pr\[ADoubleDot]zise \ mathematische Formulierung gefunden hat, n\[ADoubleDot]mlich den Begriff der \ Konvergenz bzw. des Grenzwerts einer Folge. Und wenn das so lange gedauert \ hat, dann mag es durchaus etwas l\[ADoubleDot]nger dauern, bis Sie meinen, es \ verstanden zu haben. Dazu werden ja auch noch Beispiele und \ \[CapitalUDoubleDot]bungen folgen.\ \>", "Text"], Cell[TextData[{ StyleBox["Definition 1.2.3:", FontFamily->"Arial", FontVariations->{"Underline"->True}], StyleBox[" \nG", FontFamily->"Arial"], StyleBox["RENZWERT EINER", FontFamily->"Arial", FontSize->10], StyleBox[" F", FontFamily->"Arial"], StyleBox["OLGE", FontFamily->"Arial", FontSize->10], StyleBox["\n", FontVariations->{"Underline"->True}], "Es seien ", StyleBox["a", FontSlant->"Italic"], " \[Element] \[DoubleStruckCapitalR] und ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " eine Folge. ", StyleBox["a", FontSlant->"Italic"], " hei\[SZ]t ", StyleBox["G", FontFamily->"Arial"], StyleBox["RENZWERT DER", FontFamily->"Arial", FontSize->10], StyleBox[" F", FontFamily->"Arial"], StyleBox["OLGE", FontFamily->"Arial", FontSize->10], " ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " , wenn es zu jedem ", Cell[BoxData[ \(TraditionalForm\`\[CurlyEpsilon] > 0\)]], " ein ", Cell[BoxData[ \(TraditionalForm\`n\_0\)]], " \[Element] ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalN]\)]], " gibt, so dass | ", Cell[BoxData[ \(TraditionalForm\`a\_n\ - \ a\)]], "| < \[CurlyEpsilon] f\[UDoubleDot]r alle ", StyleBox["n", FontSlant->"Italic"], " > ", Cell[BoxData[ \(TraditionalForm\`n\_0\)]], " gilt.\nMit Quantoren geschrieben sieht diese Definition so aus:\n", StyleBox["a", FontSlant->"Italic"], " hei\[SZ]t Grenzwert der Folge ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " , wenn\n\t\t", Cell[BoxData[ \(TraditionalForm\`\( \[And] \+\(\[CurlyEpsilon]\ > \ 0\)\)\)], FontSize->14], " ", Cell[BoxData[ FormBox[ StyleBox[ UnderscriptBox[\(\(\[Or]\)\(\ \)\), RowBox[{ SubscriptBox["n", StyleBox["0", FontSize->8]], " ", "\[Element]", " ", "\[DoubleStruckCapitalN]"}]], FontSize->14], TraditionalForm]]], " ", Cell[BoxData[ FormBox[ StyleBox[ UnderscriptBox["\[And]", RowBox[{"n", " ", ">", " ", SubscriptBox["n", StyleBox["0", FontSize->8]]}]], FontSize->14], TraditionalForm]]], " | ", Cell[BoxData[ \(TraditionalForm\`\(\(a\_n\)\(\ \)\(-\)\(\ \)\(a\)\(\ \)\)\)]], "| < \[CurlyEpsilon] . \n" }], "Text"], Cell[TextData[{ StyleBox["Definition 1.2.4:", FontFamily->"Arial", FontVariations->{"Underline"->True}], StyleBox[" \nK", FontFamily->"Arial"], StyleBox["ONVERGENTE", FontFamily->"Arial", FontSize->10], StyleBox[" F", FontFamily->"Arial"], StyleBox["OLGE, DIVERGENTE", FontFamily->"Arial", FontSize->10], StyleBox[" F", FontFamily->"Arial"], StyleBox["OLGE", FontFamily->"Arial", FontSize->10], StyleBox["\n", FontVariations->{"Underline"->True}], "Eine Folge ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " hei\[SZ]t ", StyleBox["KONVERGENT", FontFamily->"Arial", FontSize->10], ", wenn es ein ", StyleBox["a", FontSlant->"Italic"], " \[Element] \[DoubleStruckCapitalR] gibt, so dass ", StyleBox["a", FontSlant->"Italic"], " Grenzwert der Folge ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " ist. Eine Folge ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " hei\[SZ]t ", StyleBox["DIVERGENT", FontFamily->"Arial", FontSize->10], ", wenn sie nicht konvergent ist.\n\nDie Beweise f\[UDoubleDot]r die \ Konvergenz einer Folge k\[ODoubleDot]nnen ganz einfach sein, sie k\ \[ODoubleDot]nnen aber auch beliebig kompliziert sein. Fangen wir mit dem \ einfachsten Fall an." }], "Text"], Cell[TextData[{ StyleBox["Satz 1.2.1\n", FontFamily->"Arial", FontVariations->{"Underline"->True}], "F\[UDoubleDot]r ", StyleBox["c", FontSlant->"Italic"], " \[Element] \[DoubleStruckCapitalR] und ", StyleBox["n", FontSlant->"Italic"], " \[Element] \[DoubleStruckCapitalN] sei ", Cell[BoxData[ \(TraditionalForm\`c\_\(\(n\)\(\ \)\)\ := \ c\)]], " . Dann ist ", StyleBox["c", FontSlant->"Italic"], " Grenzwert von ", Cell[BoxData[ \(TraditionalForm\`\((c\_n)\)\)]], " .\n\n", StyleBox["Beweis:", FontFamily->"Arial"], " \nEs sei \[CurlyEpsilon] > 0 beliebig und ", Cell[BoxData[ \(TraditionalForm\`n\_0\)]], " = 1 gew\[ADoubleDot]hlt. 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Cell[TextData[{ "Als n\[ADoubleDot]chstes soll die Konvergenz der Folge ", Cell[BoxData[ \(TraditionalForm\`\((\[NegativeThinSpace]\ 1\/n\ \[NegativeThinSpace])\ \)\)]], " untersucht werden. Dazu ist das Archimedische Axiom n\[ODoubleDot]tig. Es \ ist anschaulich ganz einfach!" }], "Text"], Cell[TextData[{ "Zur Erinnerung das\n", StyleBox["\n", FontVariations->{"Underline"->True}], StyleBox["Archimedisches Axiom", FontFamily->"Arial", FontVariations->{"Underline"->True}], StyleBox["\n", FontVariations->{"Underline"->True}], "Es sei ", StyleBox["a", FontSlant->"Italic"], " \[Element] \[DoubleStruckCapitalR] . Dann gibt es ein ", Cell[BoxData[ \(TraditionalForm\`n\)]], " \[Element] ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalN]\)]], " mit ", StyleBox["n > a ", FontSlant->"Italic"], ".\n", StyleBox["\n", FontSlant->"Italic"], "Wenn ", StyleBox["a", FontSlant->"Italic"], " \[LessEqual] 0 , leistet 1 das Gew\[UDoubleDot]nschte. Ist ", StyleBox["a", FontSlant->"Italic"], " > 0 , so stellen Sie sich etwa vor, Sie h\[ADoubleDot]tten eine \ Dezimalbruchentwicklung von ", StyleBox["a", FontSlant->"Italic"], " . Dann nehmen Sie den Anteil vor dem Komma und addieren 2 dazu. So \ erhalten Sie eine nat\[UDoubleDot]rliche Zahl, die gr\[ODoubleDot]\[SZ]er als \ ", StyleBox["a", FontSlant->"Italic"], " ist. Warum reicht es nicht aus nur 1 zu addieren?\nEine andere \ Vorstellung benutzt den Zahlenstrahl, der jeweils bei den \ nat\[UDoubleDot]rlichen Zahlen markiert ist. Irgendwo \"zwischen\" zwei \ ganzen Zahlen liegt ", StyleBox["a", FontSlant->"Italic"], " , falls ", StyleBox["a", FontSlant->"Italic"], " > 0 ." }], "Text"], Cell[TextData[{ StyleBox["Satz 1.2.2", FontFamily->"Arial", FontVariations->{"Underline"->True}], StyleBox["\n", FontVariations->{"Underline"->True}], "Der Grenzwert der Folge ", Cell[BoxData[ \(TraditionalForm\`\((\[NegativeThinSpace]\ 1\/n\ \[NegativeThinSpace])\ \)\)]], " ist Null.\n", StyleBox["Beweis:", FontFamily->"Arial"], " \nEs sei \[CurlyEpsilon] > 0 . Dann gibt es nach dem Archimedischen \ Axiom ein ", Cell[BoxData[ \(TraditionalForm\`n\_0\)]], " mit ", Cell[BoxData[ \(TraditionalForm\`1\/\[CurlyEpsilon]\)]], "< ", Cell[BoxData[ \(TraditionalForm\`n\_0\)]], " . Also ist ", Cell[BoxData[ \(TraditionalForm\`1\/n\_0\)]], "< \[CurlyEpsilon] . Sei nun ", StyleBox["n", FontSlant->"Italic"], " \[GreaterEqual] ", Cell[BoxData[ \(TraditionalForm\`n\_0\)]], " . Dann folgt\n\n\t| ", Cell[BoxData[ \(TraditionalForm\`1\/n\)]], "\[Dash] 0 | = ", Cell[BoxData[ \(TraditionalForm\`1\/n\)]], "\[LessEqual] ", Cell[BoxData[ \(TraditionalForm\`1\/n\_0\)]], " < \[CurlyEpsilon] . \n" }], "Text"], Cell["\[FilledSquare]", "Text", TextAlignment->Right], Cell[TextData[{ "Es ist etwas umst\[ADoubleDot]ndlich, immer zu schreiben bzw. zu sagen: \ Der Grenzwert der Folge ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " ist ", StyleBox["a", FontSlant->"Italic"], " . Gebr\[ADoubleDot]uchlich ist die \n\n", StyleBox["Schreibweise:\n", FontFamily->"Arial", FontVariations->{"Underline"->True}], StyleBox["L", FontFamily->"Arial"], StyleBox["IMES", FontFamily->"Arial", FontSize->10], StyleBox["\n", FontVariations->{"Underline"->True}], "Es sei ", StyleBox["a", FontSlant->"Italic"], " \[Element] \[DoubleStruckCapitalR] Grenzwert der Folge ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " . Daf\[UDoubleDot]r sind folgende Schreibweisen \[UDoubleDot]blich\n\n\t \ lim ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " = ", StyleBox["a", FontSlant->"Italic"], " bzw. ", Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(\(\(lim\)\(\ \)\)\+\(n \[RightArrow] \[Infinity]\)\), "TraditionalForm"], \(a\_n\)}], TraditionalForm]]], " = ", StyleBox["a", FontSlant->"Italic"], " . \n\t \nGelesen: Der ", StyleBox["L", FontFamily->"Arial"], StyleBox["IMES", FontFamily->"Arial", FontSize->10], " der Folge ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " ist ", StyleBox["a", FontSlant->"Italic"], " ; bzw. : Der ", StyleBox["L", FontFamily->"Arial"], StyleBox["IMES", FontFamily->"Arial", FontSize->10], " von ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " f\[UDoubleDot]r ", StyleBox["n", FontSlant->"Italic"], " gegen Unendlich ist ", StyleBox["a", FontSlant->"Italic"], " ." }], "Text"], Cell[TextData[{ "Leider wird h\[ADoubleDot]ufig die folgende missverst\[ADoubleDot]ndliche \ und deshalb schlechte Sprechweise benutzt: Die Folge ", Cell[BoxData[ \(TraditionalForm\`\((a\_n)\)\)]], " strebt f\[UDoubleDot]r ", StyleBox["n", FontSlant->"Italic"], " gegen Unendlich gegen ", StyleBox["a . ", FontSlant->"Italic"], "Da strebt aber im Allgemeinen Nichts! Ich benutze deshalb auch nicht die \ kurze Schreibweise ", Cell[BoxData[ \(TraditionalForm\`a\_n\)]], "\[LongRightArrow] ", StyleBox["a", FontSlant->"Italic"], " an Stelle von ", Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(\(\(lim\)\(\ \)\)\+\(n \[RightArrow] \[Infinity]\)\), "TraditionalForm"], \(a\_n\)}], TraditionalForm]]], " = ", StyleBox["a", FontSlant->"Italic"], " .\nAuch die Formulierung \"es n\[ADoubleDot]hert sich beliebig\" ist mi\ \[SZ]verst\[ADoubleDot]ndlich, wie etwa die Folge\n\n\t", Cell[BoxData[ \(TraditionalForm\`\((\[NegativeThinSpace]\ \(1 + \((\(-1\))\)\^n\)\/n\ \ \[NegativeThinSpace])\)\)]], " = ( 0, 1, 0, ", Cell[BoxData[ \(TraditionalForm\`1\/2\)]], ", 0, ", Cell[BoxData[ \(TraditionalForm\`1\/3\)]], ", 0, ", Cell[BoxData[ \(TraditionalForm\`1\/4\)]], ", ... )\n\t\nzeigt. 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0.0162726, 0.0162726}}] }, Open ]], Cell[TextData[{ StyleBox["Beweis: ", FontFamily->"Arial"], "\nZu (", StyleBox["i", FontSlant->"Italic"], "): Es gilt ", Cell[BoxData[ \(TraditionalForm\`\(\(-a\)\(\[LessEqual]\)\)\ | \ a\ \ | \ \ , \ \(\(a\)\(\ \)\(\[LessEqual]\)\)\ | \ a\ \ | \ , \)]], " und analog ", Cell[BoxData[ \(TraditionalForm\`\(\(-b\)\(\[LessEqual]\)\)\ | \ b\ \ | \ \ , \ \(\(\(b\)\(\ \)\(\[LessEqual]\)\)\(\ \)\(|\)\(\ \)\(b\ \)\(\ \ \)\(|\)\(\ \)\)\)]], ". \nDurch Addition dieser Ungleichungen folgt\n\n\t\t\t", Cell[BoxData[ \(TraditionalForm\`\(\(-\((a\ + \ b)\)\)\(\[LessEqual]\)\)\ | \ a\ \ | \ \ \ \(+\ \(\(|\)\(\ \)\(b\)\(\ \)\(|\)\)\)\ , \ \(\(a\ + \ b\)\(\ \ \)\(\[LessEqual]\)\)\ | \ a\ \ | \ \(+\ \(\(|\)\(\ \)\(b\)\(\ \)\(|\)\(\ \)\)\)\)]], ".\n\t\t\t\nFalls | ", StyleBox["a", FontSlant->"Italic"], " + ", StyleBox["b |", FontSlant->"Italic"], " = \[Dash](", StyleBox["a", FontSlant->"Italic"], " + ", StyleBox["b", FontSlant->"Italic"], ") , so ist (", StyleBox["i", FontSlant->"Italic"], ") mit dem ersten Teil bewiesen.\nFalls | ", StyleBox["a", FontSlant->"Italic"], " + ", StyleBox["b", FontSlant->"Italic"], " | = ", StyleBox["a", FontSlant->"Italic"], " + ", StyleBox["b ", FontSlant->"Italic"], ", so ist (", StyleBox["i", FontSlant->"Italic"], ") mit dem zweiten Teil bewiesen.\n\nZu (", StyleBox["ii", FontSlant->"Italic"], "): Setze \[Alpha] := ", StyleBox["a", FontSlant->"Italic"], ", \[Beta] := \[Dash]", StyleBox["b", FontSlant->"Italic"], " . \nNach (", StyleBox["i", FontSlant->"Italic"], ") gilt | \[Alpha] + \[Beta] | \[LessEqual] | \[Alpha] | + | \[Beta] | ,\ \nalso ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(a\ - \ b\)\(|\)\)\ = \ \(\(\(|\)\(\ \)\(\[Alpha]\ + \ \[Beta]\)\(\ \ \ \)\(|\)\(\ \)\(\(\[LessEqual]\)\(\ \)\(\(|\)\(\ \)\(\[Alpha]\)\(\ \)\(|\)\(\ \ \)\(+\ \(\(|\)\(\ \)\(\[Beta]\)\(\ \)\(|\)\)\)\)\)\)\ = \ \(\(|\)\(\ \)\(a\)\ \(\ \)\(|\)\(\ \)\(+\ \(\(|\)\(\ \)\(b\)\(\ \)\( | \^\ \)\)\)\)\)\)]], " .\n\nZu (", StyleBox["iii", FontSlant->"Italic"], "): Mit (", StyleBox["i", FontSlant->"Italic"], ") folgt\n", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(a\)\(|\)\)\ = \ \(\(|\)\(\ \)\(\((a\ - \ b)\)\ + \ b\)\(|\)\(\ \)\(\(\[LessEqual]\)\(\ \)\(\(|\)\(\ \)\(a\ - \ b\)\(\ \)\(|\)\(\ \)\(+\(\(|\)\(b\)\(|\)\)\)\)\)\)\)]], " ,\n", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(b\)\(|\)\)\ = \ \(\(|\)\(\ \)\(\((b\ - \ a)\)\ + \ a\)\(|\)\(\ \)\(\(\[LessEqual]\)\(\ \)\(\(|\)\(\ \)\(a\ - \ b\)\(\ \)\(|\)\(\ \)\(+\(\(|\)\(a\)\(|\)\)\)\)\)\)\)]], " ,\nalso ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(a\)\(|\)\(\ \)\(-\ \(\(|\)\(b\)\(|\)\(\ \ \)\(\(\[LessEqual]\)\(\(|\)\(\ \)\(a\ - \ b\)\(\ \)\(|\)\)\)\)\)\)\)]], " und ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(b\)\(|\)\(\ \)\(-\ \(\(|\)\(a\)\(|\)\(\ \ \)\(\(\[LessEqual]\)\(\(|\)\(\ \)\(a\ - \ b\)\(\ \)\(|\)\)\)\)\)\)\)]], " . \nDas ergibt ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ StyleBox[ RowBox[{ StyleBox["|", FontSize->14], "|"}]], "a"}], "|", " ", RowBox[{"-", " ", RowBox[{"|", RowBox[{"b", StyleBox[ RowBox[{"|", StyleBox["|", FontSize->14]}]], " ", \(\(\[LessEqual]\)\(\(|\)\(\ \)\(a\ - \ b\)\(\ \)\(|\)\)\)}]}]}]}], TraditionalForm]]], " ." }], "Text"], Cell["\[FilledSquare]", "Text", TextAlignment->Right], Cell[TextData[{ "Es werden h\[ADoubleDot]ufig Ausdr\[UDoubleDot]cke der Gestalt ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(\ \)\(x\ - \ a\)\(\ \)\(|\)\(\ \)\(\(<\)\(\ \)\(\[CurlyEpsilon]\)\)\)\)]], " vorkommen. 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FontVariations->{"Underline"->True}], StyleBox["\n", FontVariations->{"Underline"->True}], StyleBox["Eindeutigkeit des Grenzwertes", FontFamily->"Arial"], StyleBox["\n", FontVariations->{"Underline"->True}], "Eine Folge ( ", Cell[BoxData[ \(TraditionalForm\`\(\(a\_n\)\(\ \)\)\)]], ") hat h\[ODoubleDot]chstens einen Grenzwert ", StyleBox["a", FontSlant->"Italic"], " .\n\n", StyleBox["Beweis: ", FontFamily->"Arial"], "\nDer Beweis wird indirekt gef\[UDoubleDot]hrt. Es werde angenommen, dass \ die Folge zwei Grenzwerte, etwa ", StyleBox["a", FontSlant->"Italic"], " und \[Alpha], besitze, wobei o.B.d.A. \[Alpha] > ", StyleBox["a", FontSlant->"Italic"], " sei.\nEs sei \[CurlyEpsilon] := ", Cell[BoxData[ FormBox[ StyleBox[\(\(\[Alpha]\ \[Dash]\ a\)\/2\), FontSize->16], TraditionalForm]]], " ( > 0 ) . Dann gibt es ein ", Cell[BoxData[ \(TraditionalForm\`n\_\(0 a\)\)]], " \[Element] \[DoubleStruckCapitalN] , so dass f\[UDoubleDot]r alle ", StyleBox["n", FontSlant->"Italic"], " > ", Cell[BoxData[ \(TraditionalForm\`n\_\(0 a\)\)]], " gilt\n", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(\ \)\(a\_n\ - \ a\)\(\ \)\(|\)\(\ \)\(\(<\)\(\ \)\(\[CurlyEpsilon]\)\)\)\)]], " .\nAnalog gibt es ein ", Cell[BoxData[ \(TraditionalForm\`n\_\(0 \[Alpha]\)\)]], " \[Element] \[DoubleStruckCapitalN] , so dass f\[UDoubleDot]r alle ", StyleBox["n", FontSlant->"Italic"], " > ", Cell[BoxData[ \(TraditionalForm\`n\_\(0 \[Alpha]\)\)]], " gilt ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(\ \)\(a\_n\ - \ \[Alpha]\)\(\ \)\(|\)\(\ \ \)\(\(<\)\(\ \)\(\[CurlyEpsilon]\)\)\)\)]], " .\nEs sei nun ", Cell[BoxData[ \(TraditionalForm\`n\_0\)]], " := ", Cell[BoxData[ \(TraditionalForm\`max(n\_\(0 a\)\ , \ n\_\(0 \[Alpha]\)\ )\)]], " . Dann gilt erst recht f\[UDoubleDot]r alle ", Cell[BoxData[ \(TraditionalForm\`n\ \[GreaterEqual] \ n\_0\)]], " auch ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(\ \)\(a\_n\ - \ a\)\(\ \)\(|\)\(\ \)\(\(<\)\(\ \)\(\[CurlyEpsilon]\)\)\)\)]], " und ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(\ \)\(a\_n\ - \ \[Alpha]\)\(\ \)\(|\)\(\ \ \)\(\(<\)\(\ \)\(\[CurlyEpsilon]\)\)\)\)]], " . \nNun gilt \n ", Cell[BoxData[ \(TraditionalForm\`\[Alpha]\ - \ a\ = \ \(\(\(|\)\(\ \)\(\[Alpha]\ - \ a\)\(\ \)\(|\)\)\ = \ \(\(\(|\)\(\ \)\(\[Alpha]\ - \ a\_n\ + \ a\_n\ - \ a\)\(\ \)\(|\)\)\ = \ \(\(|\)\(\ \)\(\((a\_n\ - \ a)\)\ - \ \((a\_n - \ \[Alpha]\ )\)\)\(\ \ \)\(|\)\)\)\)\)]], "\n\t", Cell[BoxData[ \(TraditionalForm\`\(\(\[LessEqual]\)\(\ \)\(\(|\)\(\ \)\(a\_n\ - \ a\)\(\ \)\(|\)\(\ \)\(+\ \(\(|\)\(\ \)\(a\_n\ - \ \[Alpha]\)\(\ \ \)\(|\)\(\ \)\(\(<\)\(\ \)\(\[CurlyEpsilon]\ + \ \[CurlyEpsilon]\)\)\)\)\)\ \)\ = \ \(2\ \[CurlyEpsilon]\ = \ \[Alpha]\ - \ a\)\)]], " , \nd.h. ", Cell[BoxData[ \(TraditionalForm\`\[Alpha]\ - \ a\ < \ \[Alpha]\ - \ a\)]], " , was ein klassischer Widerspruch ist. \nAlso kann eine Folge h\ \[ODoubleDot]chstens einen Grenzwert besitzen." }], "Text"], Cell["\[FilledSquare]", "Text", TextAlignment->Right], Cell[TextData[{ StyleBox["Beachten Sie", FontFamily->"Arial", FontWeight->"Bold"], StyleBox[":", FontFamily->"Arial"], " Mit diesem Satz ist ", StyleBox["aber \[UDoubleDot]berhaupt nicht", FontWeight->"Bold"], " gezeigt, dass eine Folge einen Grenzwert besitzt. Nehmen Sie z.B. ", Cell[BoxData[ \(TraditionalForm\`\((\[NegativeThinSpace]\ \((\(-1\))\)\^n\ \ \[NegativeThinSpace])\)\)]], " ! 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Es sei \[CurlyEpsilon] := 1 . Dann gibt es ein ", Cell[BoxData[ \(TraditionalForm\`n\_0\)]], " , so dass f\[UDoubleDot]r alle ", StyleBox["n", FontSlant->"Italic"], " > ", Cell[BoxData[ \(TraditionalForm\`n\_0\)]], " gilt ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(\ \)\(a\_n\ - \ a\)\(\ \)\(|\)\(\ \)\(\(<\)\(\ \)\(\[CurlyEpsilon]\)\)\)\)]], " = 1. Mit der Dreiecksungleichung folgt daraus\n\t", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(\ \)\(a\_n\)\(\ \)\(|\)\(\ \)\(-\ \(\(|\)\(\ \ \)\(a\)\(\ \)\(|\)\(\ \)\(\(\[LessEqual]\)\(\ \)\(\(|\)\(\ \)\(a\_n\ - \ a\)\(\ \)\(|\)\(\ \)\(\(<\)\(\ \)\(1\)\)\)\)\)\)\)\)]], " , also", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(\ \)\(a\_n\)\(\ \)\(|\)\(\ \)\(\(<\)\(\ \ \)\(\(|\)\(\ \)\(a\)\(\ \)\(|\)\(\ \)\(+\ 1\)\)\)\)\)]], " . \nEs sei nun\n\t", StyleBox["M", FontSlant->"Italic"], " := max{ ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(a\_1\)\(|\)\), \ \(\(|\)\(a\_2\)\(|\)\), \ \ ... \ , \ \(\(|\)\(a\_\(n\_0\)\)\(|\)\), \ \(\(|\)\(a\)\(\ \)\(|\)\(+\ 1\)\)\)]], " } . \nDann gilt f\[UDoubleDot]r alle ", Cell[BoxData[ \(TraditionalForm\`a\_m\)]], " , dass ", Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(a\_m\)\(|\)\(\(<\)\(\ \)\(M\)\)\)\)]], ", d.h. ", StyleBox["(", FontSize->14], Cell[BoxData[ \(TraditionalForm\`\(\(|\)\(\ \)\(a\_n\)\(|\)\)\)]], StyleBox[")", FontSize->14], " ist beschr\[ADoubleDot]nkt und damit auch ( ", Cell[BoxData[ \(TraditionalForm\`\(\(a\_n\)\(\ \)\)\)]], ") ." }], "Text"], Cell["\[FilledSquare]", "Text", TextAlignment->Right], Cell["\<\ Bevor einige weitere Folgen auf Konvergenz untersucht werden sollen, noch der\ \ \>", "Text"], Cell[TextData[{ StyleBox["Satz 1.2.6\n", FontFamily->"Arial", FontVariations->{"Underline"->True}], StyleBox["B", FontFamily->"Arial"], StyleBox["ERNOULLI", FontFamily->"Arial", FontSize->10], StyleBox["sche Ungleichung", FontFamily->"Arial"], StyleBox["\n", FontVariations->{"Underline"->True}], "(", ButtonBox["Jacob Bernoulli", ButtonData:>{ URL[ "http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Bernoulli_\ Jacob.html"], None}, ButtonStyle->"Hyperlink"], ", 1654 - 1705, Schweizer Mathematiker)\n\nEs sei ", StyleBox["n", FontSlant->"Italic"], " \[Element] ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalN]\_0\)]], " und ", StyleBox["x", FontSlant->"Italic"], " > \[Dash]1 . Dann gilt \n\n(", StyleBox["i", FontSlant->"Italic"], ")\t", Cell[BoxData[ \(TraditionalForm\`\((1\ + \ x)\)\^n\ \[GreaterEqual] \ 1\ + \ n\ x\)]], " .\n\nIst noch ", StyleBox["n", FontSlant->"Italic"], " > 1 und ", StyleBox["x", FontSlant->"Italic"], " > 0, so gilt\n\n(", StyleBox["ii", FontSlant->"Italic"], ")\t", Cell[BoxData[ \(TraditionalForm\`\((1\ + \ x)\)\^n\ > \ 1\ + \ n\ x\)]], " .\n\n", StyleBox["Beweis durch vollst\[ADoubleDot]ndige Induktion: ", FontFamily->"Arial"], "\nF\[UDoubleDot]r ", StyleBox["n", FontSlant->"Italic"], " = 0 ist (", StyleBox["i", FontSlant->"Italic"], ") richtig. Es sei nun ", StyleBox["x", FontSlant->"Italic"], " \[NotEqual] 0 .\n", StyleBox["I: Induktionsanfang:", FontFamily->"Arial"], "\n\tF\[UDoubleDot]r ", StyleBox["n", FontSlant->"Italic"], " = 0 gilt ", Cell[BoxData[ \(TraditionalForm\`\((1\ + \ x)\)\^0\ = 1 \[GreaterEqual] \ 1\ + \ 0\ x\)]], " ;\n \tf\[UDoubleDot]r ", StyleBox["n", FontSlant->"Italic"], " = 1 gilt ", Cell[BoxData[ \(TraditionalForm\`\((1\ + \ x)\)\^1\ = 1\ + \ 1\ x\)]], " ; ,\n\tund f\[UDoubleDot]r ", StyleBox["n", FontSlant->"Italic"], " = 2 gilt ", Cell[BoxData[ \(TraditionalForm\`\((1\ + \ x)\)\^2\ = 1 + \ 2 x\ + \ x\^2\ > \ 1\ + \ 2\ x\)]], " .\n\t\n\n", StyleBox["II: Induktionsschritt:", FontFamily->"Arial"], "\nInduktionsvoraussetzung:\n\tF\[UDoubleDot]r ein ", StyleBox["n", FontSlant->"Italic"], " \[GreaterEqual] 1 gelte ", Cell[BoxData[ \(TraditionalForm\`\((1\ + \ x)\)\^n\ \[GreaterEqual] \ 1\ + \ n\ x\)]], " . \nInduktionsbehauptung: \n\tDann gilt ", Cell[BoxData[ \(TraditionalForm\`\((1\ + \ x)\)\^\(n + 1\)\ \[GreaterEqual] \ 1\ + \ \((n\ + \ 1)\)\ x\)]], " .\n", StyleBox["Beweis daf\[UDoubleDot]r:", FontFamily->"Arial"], "\n\t ", Cell[BoxData[{ \(TraditionalForm\`\((1\ + \ x)\)\^\(n + 1\)\ = \ \(\((1\ + \ x)\)\^n\) \((1\ + \ x)\) \[GreaterEqual] \ \(\((1\ + \ n\ \ x)\) \((1\ + \ x)\)\(\ \)\)\), "\[IndentingNewLine]", \(TraditionalForm\`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(\(\(=\)\(\ \)\(1\ + \ x\ + \ n\ x\ + \ n\ x\^2\ > \ 1\ + \ \((n\ + \ 1\ )\)\ x\)\)\(\ \ \)\(,\)\)\)}]], " \nwas zu beweisen war. \ " }], "Text"], Cell["\<\ Zwei Grafiken zur Bernoullischen Ungleichung: \ \>", "Text"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.339146 0.318522 0.0561849 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