{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 1 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 -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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 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 -1 54 "Armando H\344ring (12) Is ollde-Kurz-Gymnasium,Reutlingen" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 51 "Kurvendiskussion einer gebrochenrationalen Funktion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Die zu untersuchende Funktion eingeben." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f:=x->(x^2-4*x+3)/(x-2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"xG6\"6$%)operatorG%&ar rowGF(*&,(*$9$\"\"#\"\"\"F/!\"%\"\"$F1F1,&F/F1!\"#F1!\"\"F(F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Der Nenner der gebrochenrationalen Funktion wird als Funktion N(x) festgelegt. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "N:=unapply(denom(f(x)),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG:6#%\"xG6\"6$%)operatorG%&arrowGF(,&9$\"\"\"!\"#F .F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Der Z\344hler der gebroc henrationalen Funktion wird als Funktion Z(x) festgelegt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Z:=unapply(numer(f(x)),x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG:6#%\"xG6\"6$%)operatorG%&arrowG F(,(*$9$\"\"#\"\"\"F.!\"%\"\"$F0F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Darstellung des Nenner und des Z\344hlerpolynoms:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "plot(\{Z(x),N(x)\},x=-5..5,-5..5,ti tle=`Nenner und Z\344hlerpolynom`);" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 12 "Ableitungen:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Erst e und zweite Ableitung mit jeweiliger Polynomdivision:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 229 "fs:=D(f):\n`Erste Ableitung`:=simp lify(fs(x));\n`Erste Ableitung mit Polynomdivision`:= convert(fs(x),pa rfrac,x);\nfss:=D(fs):\n`Zweite Ableitung`:=simplify(fss(x));\n`Zweite Ableittung mit Polynomdivision`:=convert(fss(x),parfrac,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%0Erste~AbleitungG*&,(*$%\"xG\"\"#\"\"\"F(! \"%\"\"&F*F*,&F(F*!\"#F*F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%DErste ~Ableitung~mit~PolynomdivisionG,&\"\"\"F&*$,&%\"xGF&!\"#F&F*F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%1Zweite~AbleitungG,$*$,&%\"xG\"\"\"! \"#F)!\"$F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%FZweite~Ableittung~mi t~PolynomdivisionG,$*$,&%\"xG\"\"\"!\"#F)!\"$F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Darstellung der ersten und zweiten Ableitung:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "plot(\{`Erste Ableitung`,`Z weite Ableitung`\},x=-50..50,-50..50,title=`Erste und zweite Ableitung der Funktion`);" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 11 "Assymptotik " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Die Gleichung der Assymptote \+ wird aufgestellt und durch einen plot dargestellt:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "f:=unapply(convert(f(x),parfrac,x),x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"xG6\"6$%)operatorG%&arrowG F(,(9$\"\"\"!\"#F.*$,&F-F.F/F.!\"\"F2F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 44 "rem(x^2-4*x+3,x-2,x,Assymptote):\nAssymptote;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"\"!\"#F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "plot(Assymptote,x,title=`Assymptote der F unktion`);" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 25 "Nullstellen des Z \344hlers :" }}{PARA 0 "" 0 "" {TEXT -1 45 "Die Nullstellen des Z\344h lers werden errechnet:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "N ullstellen[z\344hler]:=[solve(Z(x))];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%,NullstellenG6#%'z|_yhlerG7$\"\"\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Nullstellen[z\344hler][1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 29 "Defini tionsl\374cke des Nenners:" }}{PARA 0 "" 0 "" {TEXT -1 47 "Die Definit ionl\374cke des Nenners wird errechnet:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Definitionsluecken[nenner]:=solve(N(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%3DefinitionslueckenG6#%'nennerG\"\"#" }}} {EXCHG {PARA 261 "" 0 "" {TEXT -1 8 "Extrema:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Berechnung der Extremas:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "Extrem:=[solve(fs(x))];\nAnzahl[E]:=nops(Extrem);\nf or i from 1 to Anzahl[E] do Extremstelle[i]:=[Extrem[i],f(Extrem[i])] \+ od;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'ExtremG7$,&\"\"#\"\"\"%\"I GF(,&F'F(F)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'AnzahlG6#%\"EG \"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%-ExtremstelleG6#\"\"\"7$,& \"\"#F'%\"IGF',$F+F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%-Extremstel leG6#\"\"#7$,&F'\"\"\"%\"IG!\"\",$F+!\"#" }}}{EXCHG {PARA 262 "" 0 "" {TEXT -1 12 "Wendepunkte:" }}{PARA 0 "" 0 "" {TEXT -1 27 "Berechnung d er Wendepunkte:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "Wend:=[ solve(fss(x))];\nAnzahl[W]:=nops(Wend);\nfor i from 1 to Anzahl[W] do \+ Wendestelle[i]:=[Wend[i],f(Wend[i])] od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%WendG7\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'AnzahlG6#%\"W G\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 11 "Darstellung" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "display(plot(\{f(x),Z(x),N(x ),fs(x),fss(x)\},x=-20..20,-20..20),title=`Komplette Darstellung` );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Armando.Haering@ikg.rt.bw.schul e.de" }}}}{MARK "1 0 0" 11 }{VIEWOPTS 1 1 0 1 1 1803 }