{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "" -1 256 "" 1 18 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 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 18 0 0 0 0 0 1 1 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 }{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 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2 " -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "Name: Alexandra Buck \+ " }}{PARA 0 "" 0 "" {TEXT -1 15 "Datum: 06.06.02" }}{PARA 0 "" 0 "" {TEXT -1 56 "Thema: Kurvendiskussion einer parametrisierten Funktio n " }}{PARA 0 "" 0 "" {TEXT -1 184 "Stichworte: Kurvendiskussion nach \+ Schema (Ableitung, Nullstellen, usw...), Gemeinsame Punkte, \+ Ortskurve von Waagepunkten, DGL zur Schar, Isoklinen, Fl\344ch enberechnung." }}{PARA 0 "" 0 "" {TEXT 256 19 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 28 " \+ " }{TEXT 262 16 "Kurvendiskussion" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "Parametris ierte Funktion:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f:=x->1/2*x+1/2*t+t/x;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 263 20 "1. und 2. Ableitung." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f1:=unapply(diff(f(x),x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f2:=unapply(diff(f1(x),x),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 264 12 "Nullstellen:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(f (x)=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "Nullstelen liegen al so bei N[0/-1/2*t+/-1/2*sqrt(t^2-8*t)]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 265 14 "Extremstelle n:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ex:=solve(f1(x)=0,x);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "a:=subs(x=ex[1],f2(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "=> Tiefpunkt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "b:=subs(x=ex[2],f2(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "=> Hochpunkt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "yw1:=f (ex[1]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "yw2:=f(ex[2]); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 266 13 "Wendestellen:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(f2(x)=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Es gibt keine Wendestelle." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "p1:=plot([seq(f(x),t=-2..2)],x=-5..5,y=-5..5):p1;" }} {PARA 13 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 258 17 "Gemeinsame Punkte" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Gibt es gemeinsame Punkt ?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "ft:=diff(f(x),t);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(ft=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Bei x=-2 haben die Scharkurven einen geme insamen Punkt." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 0 {PARA 256 "" 0 "" {TEXT -1 7 "Ortskur" }{TEXT 259 0 "" }{TEXT -1 19 "ve der Waagepunkte:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "tw1:=solve(ex[1]=x,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "tw2:=solve(ex[2]=x,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "c:=subs(t=tw1,yw1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " k:=subs(t=tw2,yw2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "OK durch T iefpunkte:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "OKT:=unapply( c,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "OK durch Hochpunkte:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "OKT:=unapply(k,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 260 10 "Isoklinen: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "tc:=solve(f1(x)=c,t);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "ik:=unapply(subs(t=tc,f(x) ),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 261 14 "DGL zur Schar:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "solve(\{y=f(x),ys=f1(x)\},\{t,ys\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 256 "" 0 "" {TEXT -1 18 "Fl\344chenberechnung:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart;with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "t1:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "t2 :=-3/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "ft1:=x->1/2*x+1/ 2*1+1/x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "ft2:=x->1/2*x+1 /2*(-3/2)+(3/2)/x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "pt1:= plot(ft1(x),x=-5..5,y=-5..5):pt1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "pt2:=plot(ft2(x),x=-5..5,y=-5..5):pt2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display(pt1,pt2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "int((ft2(x)-ft1(x)),x=0..5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int((ft2(x)-ft1(x)),x=-5..0);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Die Fl\344che geht also in +/- une ndlich." }{MPLTEXT 1 0 1 "\n" }}}{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 "3" 0 }{VIEWOPTS 1 1 0 1 1 1803 }