{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 9 "L'Hopital" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "T\346ller f(x) og n \346vner g(x), og x->a defineres" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=x->sinh(x^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%%sinhG6#*$)9$\"\"#\"\"\"F(F( F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "g:=x->cos(x)-1;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrow GF(,&-%$cosG6#9$\"\"\"F1!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "f(x) differentieret 1, 2 og 3 g ange:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(f(x),x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#\"\"\"-%%coshG6#*$)%\"xGF%F&F &F,F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(f(x),x$2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"\"%\"\"\"-%%sinhG6#*$)%\"xG \"\"#F&F&F+F&F&*&F-F&-%%coshGF)F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(f(x),x$3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,& *(\"\")\"\"\"-%%coshG6#*$)%\"xG\"\"#F&F&)F,\"\"$F&F&*(\"#7F&-%%sinhGF) F&F,F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "g(x) differentieret 1 ,2 og 3 gange:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(g(x) ,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$sinG6#%\"xG!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(g(x),x$2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$cosG6#%\"xG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(g(x),x$3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "V\346rdier i nds\346ttes. Der hvor t\346ller eller n\346vner er forskellig fra nul \+ stoppes." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "0. differentation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ev al(subs(x=a,f(x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eval(subs(x=a,g(x)));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "1. differentation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "eval(subs(x=a,diff(f(x),x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "eval(subs(x=a,d iff(g(x),x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "2. differentation" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 31 "eval(subs(x=a,diff(f(x),x$2)));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "eval(subs(x=a,diff(g(x),x$2)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "3. differentation" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "eval(subs(x=a,diff(f(x),x$3) ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "eval(subs(x=a,diff(g(x),x$3)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "(for ts\346t evt.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 256 "" 0 "" {TEXT -1 8 "Kontrol:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(f(x)/g(x),x=a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "29 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }