{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 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 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 6 "Quelle" }}{EXCHG {PARA 0 " " 0 "" {TEXT -1 287 "Dateiname: fktung.mws\nDateigr\366\337e: 7 KB\nNa me: Christoph Schill\nSchule: Isolde-Kurz-Gymnasium\nKlasse: 11 D\nDat um: 12.11.97\nFach: Mathematik\nThema: Funktionsuntersuchung\nStichw \366rter: gebrochene rationale Funktionen\nKurzbeschreibung: Beschreib ung einer vollstaendigen Funktionsuntersuchung \n" }}}}{EXCHG {PARA 256 "" 0 "" {TEXT 256 50 "Beispiel einer vollst\344ndigen Funktionsunt ersuchung" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "Funktion" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "rest art:with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f:=x->( x^2)/(x-4);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "Definitionsmenge " }}{EXCHG {PARA 0 "" 0 "" {TEXT 257 19 "1.Definitionsmenge:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(denom(f(x))=0,x);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Die Menge besteht aus allen ration alen Zahlen, au\337er dieser(n)." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "Symetrie" }}{EXCHG {PARA 0 "" 0 "" {TEXT 258 11 "2.Symetrie:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 206 "Loe1:=`Achsenssymetrisch z ur y-Achse`:\nLoe2:=`Punktsymetrisch zum Ursprung`:\nLoe3:=`Keine Syme trie`:\nif f(-x)=f(x) then Loe1 fi;\nif f(-x)= -f(x) then Loe2 fi;\nif f(-x)<>f(x) and f(-x)<> -f(x) then Loe3 fi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Polste llen" }}{EXCHG {PARA 0 "" 0 "" {TEXT 259 36 "3.Polstellen; senkrechte \+ Asymptoten:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(denom( f(x))=0,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 34 "Verschieden Verhalten bei gro\337en x" }}{EXCHG {PARA 0 "" 0 "" {TEXT 260 22 "4.Verhalten f\374r x-> + " } {XPPEDIT 18 0 "infinity" "I)infinityG6\"" }{TEXT 261 9 " und x->-" } {XPPEDIT 18 0 "infinity" "I)infinityG6\"" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Poly:=f(x)=convert(f(x),parfrac,x); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Es gibt eine " }{TEXT 267 20 "waagrechte Asymptote" }{TEXT -1 66 ", falls der Grad des Z\344hlers n icht gr\366\337er ist als der des Nenners," }}{PARA 0 "" 0 "" {TEXT 268 17 "schiefe Asymptote" }{TEXT -1 70 ", falls der Grad des Z\344hle rs um 1 gr\366\337er ist als der Grad des Nenners." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "N ullstellen" }}{EXCHG {PARA 0 "" 0 "" {TEXT 262 14 "5.Nullstellen:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Nullstellen:=\{solve((f(x))= 0,x)\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Anzahl1:=nops(Nu llstellen);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "for i from 1 to Anzahl1 do\nNst[i]:=[Nullstellen[i],f(Nullstellen[i])] od;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "N:=plot(\{seq(Nst[o],o=1..An zahl1)\},style=point,symbol=box,color=green,thickness=5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Ableitungen" }}{EXCHG {PARA 0 "" 0 "" {TEXT 263 14 "6.Ableitung en:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f1:=D(f);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f2:=D(f1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 7 "Extrema " }}{EXCHG {PARA 0 "" 0 "" {TEXT 264 16 "7.Extremstellen:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Extrema:=\{solve(f1(x)=0,x)\};" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Anzahl2:=nops(Extrema);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "for e from 1 to Anzahl2 do\n Ext[e]:=[Extrema[e],f(Extrema[e])] od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "E:=plot(\{seq(Ext[q],q=1..Anzahl2)\},style=point,symb ol=box,color=green,thickness=5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Wendestelle n" }}{EXCHG {PARA 0 "" 0 "" {TEXT 265 15 "8.Wendestellen:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Wendestellen:=\{fsolve(f2(x)=0,x)\} ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Anzahl3:=nops(Wendeste llen);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "for t from 1 to A nzahl3 do\nWen[t]:=[Wendestellen[t],f(Wendestellen[t])] od;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "W:=plot(\{seq(Wen[w],w=1..An zahl3)\},style=point,symbol=box,color=green,thickness=5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Schaubild" }}{EXCHG {PARA 0 "" 0 "" {TEXT 266 13 "9.Schaubilder " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 220 "Zaehler:=plot(numer(f( x)),x=-8..8,-8..8,title=`Vollstaendige Funtionsuntersuchung`): Nenner: =plot(denom(f(x)),x=-8..8,-8..8,color=green):\nKurve:=plot(f(x),x,colo r=blue,thickness=3):\ndisplay(\{N,E,W,Zaehler,Nenner,Kurve\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "7" 0 } {VIEWOPTS 1 1 0 1 1 1803 }