{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "limit(x^n*exp(-x),x= infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(x^n*ln( x),x=0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assume(n>0);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(x^n*ln(x),x=0);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(exp(-1/x^2),x=-10..10); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(exp(-1/x^2),x=-1.. 1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(exp(-1/x^2),x=- 0.1..0.1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "n:='n':" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 256 50 "Fl\344chenbestimmung durch arithm etrische Zerlegungen" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "Links:=proc(f,x,a,b,n)\nsum(eval(f,x=a+k*(b-a)/n)*(b- a)/n,k=0..n-1) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Link s(x^2,x,a,b,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "limit(Li nks(x^2,x,a,b,n),n=infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "Linksintegral:=proc(f,x,a,b) limit(Links(f,x,a,b,n),n=infinity) \+ end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Linksintegral(x^3,x ,a,b,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Linksintegral(x ^4,x,a,b,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "res:=Linksi ntegral(x^alpha,x,a,b,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Linksintegral(1/x,x,a,b,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "limit(res,alpha=-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Linksintegral(exp(x),x,a,b,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Linksintegral(x*exp(x),x,a,b,n);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 35 "res:=Linksintegral(sin(x),x,a,b,n);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(res);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "res:=Linksintegral(cos(x),x,a,b,n); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(res);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "res:=Linksintegral(x*cos(x), x,a,b,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(res); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Linksintegral(tan(x),x, a,b,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Linksintegral(lo g(x),x,a,b,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Linksinte gral((1+x)/(1-x),x,a,b,n);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 48 "Fl \344chenbestimmung durch geometrische Zerlegungen" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "Linksgeom:=proc(f,x,a,b, n)\nsum(eval(f,x=a*(b/a)^(k/n))*(a*(b/a)^((k+1)/n)-a*(b/a)^(k/n)),k=0. .n-1) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "Linksgeominte gral:=proc(f,x,a,b) limit(Linksgeom(f,x,a,b,n),n=infinity) end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "assume(a>0); assume(b>0);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Linksgeomintegral(x,x,a,b) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Linksgeomintegral(x^2, x,a,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Linksgeomintegra l(x^3,x,a,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Linksgeomi ntegral(x^alpha,x,a,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " Linksgeomintegral(1/x,x,a,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "simplify(Linksgeom(1/x,x,a,b,n));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "limit(n*((b/a)^(1/n)-1),n=infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "res:=Linksgeomintegral(ln(x),x,a,b) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(res);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Linksgeomintegral((1+x)/(1-x ),x,a,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "res:=Linksgeom integral(sin(x)*exp(x),x,a,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(res);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "i nt(sin(x)*exp(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 2 1 1805 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }