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"6#/7$,$*&I\"tG6\"\" \"$,&-I$absGI*protectedGF-6#F'F)!\"'\"\"\"!\"\"F1,&*$F'\"\"##F0F4F+!\" $F$" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 9 "e valb(%);" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#I%trueGI*protectedGF$" } {TEXT 203 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 205 49 "On en d\351du it la r\351duction du domaine d'\351tude aux " }{TEXT 206 19 "param\35 0tres positifs" }{TEXT 205 36 ", le reste du support s'obtient par " } {TEXT 206 17 "sym\351trie / \340 (Oy)" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 204 15 "Vecteur \+ vitesse" }{TEXT 205 0 "" }}{PARA 203 "" 0 "" {TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 13 "assume(t>=0);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 8 "\"x'(t)\"=" }{MPLTEXT 1 202 40 "factor (D(x)(t));\"y'(t)\"=factor(D(y)(t));" }{MPLTEXT 1 202 0 "" }}{PARA 204 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#/Q& x'(t)6\",$*(I#t|irGF%\"\"#,&F(\"\"\"!\"$F+F+,&F(F+!\"#F+F.#F)\"\"$" } {TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#/Q&y'(t)6\",&I#t|irG F%\"\"\"!\"$F(" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 205 22 "Au point stationnaire " } {TEXT 206 35 "M(3) on a une tangente de pente 1/6" }{TEXT 205 0 "" }} {PARA 201 "" 1 "" {TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 4 "ta:=" }{MPLTEXT 1 202 124 "factor((y(t)-y(3))/(x(t)- x(3))):('y'(t)-'y'(3))/('x'(t)-'x'(3))=ta;Limit(('y'(t)-'y'(3))/('x'(t )-'x'(3)),t=3)=limit(ta,t=3);" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 " " {XPPMATH 20 "6#/*&,&-I\"yG6\"6#I#t|irGF(\"\"\"-F'6#\"\"$!\"\"F+,&-I \"xGF(F)F+-F2F-F/F/,$*&,&F*F+!\"#F+F+,&F*F+\"\"'F+F/#F.\"\"#" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#/-I&LimitG6$I*protectedGF' I(_syslibG6\"6$*&,&-I\"yGF)6#I#t|irGF)\"\"\"-F.6#\"\"$!\"\"F1,&-I\"xGF 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"> " 0 "" {MPLTEXT 1 202 44 "Limit('x'(t),t=2,left)=l imit(x(t),t=2,left);" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#/-I&LimitG6$I*protectedGF'I(_syslibG6\"6%-I\"xGF)6#I#t| irGF)/F.\"\"#I%leftGF),$I)infinityGF'!\"\"" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 34 "Limit('y'(t),t=2)=limit(y(t),t= 2);" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#/-I&Limit G6$I*protectedGF'I(_syslibG6\"6$-I\"yGF)6#I#t|irGF)/F.\"\"#!\"%" } {TEXT 203 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 205 9 "D'o\371 une " }{TEXT 206 21 "asymptote horizontale" }{TEXT 205 12 " d'\351quation " }{TEXT 206 4 "y=-4" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 205 2 "La" } {TEXT 206 19 " position relative " }{TEXT 205 19 "\351tant donn\351 pa r le " }{TEXT 206 22 "signe de la diff\351rence" }{TEXT 205 3 " de" }} {PARA 203 "" 0 "" {TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 22 "delta:=factor(y(t)+4);" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I&deltaG6\",$*&,&I#t|irGF%\"\"\"!\"#F*F*,&F)F*!\"%F*F* #F*\"\"#" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 43 "pos:=H(delta):plot(pos,t=1..3,thickness=2);" }}{PARA 206 "" 1 "" {GLPLOT2D 400 400 400 {PLOTDATA 2 "6&-%'CURVESG6$7hn7$$\"\"\"\"\"!F (7$$\"3ALLL3VfV5!#LLezs$HL\"F.F(7$$\"31++D@1Bv8F.F(7$$\"3pmmm@Xt=9F.F(7$$\" 3MLL$3y_qX\"F.F(7$$\"3'******\\1!>+:F.F(7$$\"3*******\\Z/Na\"F.F(7$$\" 35+++NfC&e\"F.F(7$$\"3LLLez6:B;F.F(7$$\"3_mmm\"=C#o;F.F(7$$\"3gmmmEpS1 F.F(7$$\"3mmm\"zihl&>F.F(7$$\"35+ ]PCsyx>F.F(7$$\"3KLL$3#G,**>F.F(7$$\"3#3Fp^y!R+?F.$!\"\"F*7$$\"3L3_] \\(o<+#F.Fdp7$$\"3%e9TQrYJ+#F.Fdp7$$\"3N$3x\"yY_/?F.Fdp7$$\"3Pe*[og!G2 ?F.$!3A+++++++5F.7$$\"3RL3_Nl.5?F.Fdp7$$\"3V$ekGR[b,#F.Fdp7$$\"3YL$3-D g5-#F.Fdp7$$\"3aLe*['R3K?F.Fdp7$$\"32" } {TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}} {EXCHG {PARA 203 "" 0 "" {TEXT 204 19 "Etude en +inifinity" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 35 "Limit('x'(t),t=infinity)=limit( x(t)" }{MPLTEXT 1 202 11 ",t=infinity" }{MPLTEXT 1 202 2 ");" } {MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#/-I&LimitG6$I*p rotectedGF'I(_syslibG6\"6$-I\"xGF)6#I#t|irGF)/F.I)infinityGF'F0" } {TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 12 "Limit( 'y'(t)" }{MPLTEXT 1 202 11 ",t=infinity" }{MPLTEXT 1 202 12 ")=limit(y (t)" }{MPLTEXT 1 202 11 ",t=infinity" }{MPLTEXT 1 202 2 ");" } {MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#/-I&LimitG6$I*p rotectedGF'I(_syslibG6\"6$-I\"yGF)6#I#t|irGF)/F.I)infinityGF'F0" } {TEXT 203 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 205 9 "D'o\371 une " }{TEXT 206 15 "branche infinie" }{TEXT 205 10 " lorsque " }{TEXT 206 10 "t->+infini" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 32 "' y'(t)/'x'(t)=factor(y(t)/x(t));" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#/* 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{MPLTEXT 1 202 68 "Limit('y'(t)-3*'x'(t)/2,t=infinity)=l imit(y(t)-3*x(t)/2,t=infinity);" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#/-I&LimitG6$I*protectedGF'I(_syslibG6\"6$,&-I\"yGF )6#I#t|irGF)\"\"\"-I\"xGF)F.#!\"$\"\"#/F/I)infinityGF',$F7!\"\"" } {TEXT 203 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 205 20 "Il s'agit don c d'une" }{TEXT 206 39 " branche parabolique de direction y=3/2" } {TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> \+ " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 204 20 "S upport de la courbe" }{TEXT 205 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 205 0 "" }}}{SECT 1 {PARA 205 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 19 "t:='t':with(plots):" }}{PARA 207 "" 1 "" {TEXT 208 49 "Warning, the name changecoords has been rede fined" }{TEXT 208 0 "" }}}{EXCHG {PARA 201 "" 1 "" {XPPMATH 20 "6#7fnI 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