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211 "Times" 1 12 0 0 0 1 2 1 1 2 2 2 0 0 0 1 } {PSTYLE "_pstyle7" -1 206 1 {CSTYLE "" -1 -1 "MS Serif" 1 18 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }1 1 0 -1 8 4 1 0 1 0 2 2 -1 1 }{PSTYLE "_pstyle8" -1 207 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "_pstyle9" -1 208 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }3 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{CSTYLE "_cstyle11" -1 212 "Times" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }{PSTYLE "_pstyle10" -1 209 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{CSTYLE "_ cstyle12" -1 213 "Times" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 31 "restart;with(plo ts):secu:=1000:" }{TEXT 203 4 "secu" }{TEXT 204 60 " une valeur de s\3 51curit\351 pour \351viter les boucles trop longues" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {TEXT 205 49 "Warning, the name changecoords \+ has been redefined" }{TEXT 205 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 206 10 "Exercice 1" }{TEXT 207 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 208 11 "Question a)" }{TEXT 207 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 31 " Dichotomie:=proc(f,a,b,epsilon)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 29 "\nlocal aa,bb,compteur,milieu;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\naa:=a;bb:=b;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 2 "\n " } {TEXT 204 79 "avant d'amorcer la boucle assurons-nous que nous sommes \+ dans un cas particulier" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 55 "\n i f is(f(a)*f(b)>0) then return([infinity,infinity]); " }{TEXT 204 67 "s i f(a) et f(b) sont de m\352me signe on renvoie une solution erronn\35 1e" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 38 "\n elif is(f(a)=0) then r eturn([0,a]); " }{TEXT 204 30 "si f(a)=0 alors a est solution" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 37 "\n elif is(f(b)=0) then return ([0,b]);" }{TEXT 204 31 " si f(b)=0 alors b est solution" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nfi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\ncompteur:=0;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 54 "\nwhi le is(abs(bb-aa)>epsilon) and is(compteur " 0 "" {MPLTEXT 1 202 0 " " }}}{EXCHG {PARA 203 "" 0 "" {TEXT 208 11 "Question b)" }{TEXT 207 0 "" }}}{EXCHG {PARA 204 "> " 0 "" {MPLTEXT 1 202 0 "" }}{PARA 204 "> " 0 "" {MPLTEXT 1 202 0 "" }}{PARA 204 "> " 0 "" {TEXT 209 15 "Premier e xemple" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 46 "f:=x->exp(-x /2)-1;a:=-4;b:=4;epsilon:=10^(-8);" }{MPLTEXT 1 202 0 "" }}{PARA 205 " " 1 "" {XPPMATH 20 "6#>I\"fG6\"f*6#I\"xGF%F%6$I)operatorGF%I&arrowGF%F %,&-I$expGF%6#,$9$#!\"\"\"\"#\"\"\"F3F5F%F%F%" }{TEXT 210 0 "" }} {PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"aG6\"!\"%" }{TEXT 210 0 "" }} {PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"bG6\"\"\"%" }{TEXT 210 0 "" }} {PARA 205 "" 1 "" {XPPMATH 20 "6#>I(epsilonG6\"#\"\"\"\"*++++\"" } {TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 31 "sol:=D ichotomie(f,a,b,epsilon);" }{TEXT 203 8 "solution" }{TEXT 204 36 " pro pos\351 par la proc\351dure Dichotomie" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I$solG6\"7$\"#I#!+B=ut5\"*caVo#" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 30 "'f'(sol[2])= evalf(f(sol[2])); " }{TEXT 203 12 "valeur de f " }{TEXT 204 11 "en ce \+ point" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#/-I\"fG 6\"6##!+B=ut5\"*caVo#$\"+%3c!*Q'!\"*" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 204 "> " 0 "" {TEXT 209 16 "Deuxi\350me exemple" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 47 "f:=x->x^3-4*x+1;a:=-2.5;b:=-2;epsilon:=10^(-8);" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"fG6\"f*6#I\"xGF%F%6$ I)operatorGF%I&arrowGF%F%,(*$9$\"\"$\"\"\"F.!\"%F0F0F%F%F%" }{TEXT 210 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"aG6\"$!#D!\"\"" } {TEXT 210 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"bG6\"!\"#" } {TEXT 210 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I(epsilonG6\"#\"\" \"\"*++++\"" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 31 "sol:=Dichotomie(f,a,b,epsilon);" }{TEXT 203 8 "solution" } {TEXT 204 36 " propos\351 par la proc\351dure Dichotomie" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I$solG6\"7$\"#E$!+Wv!\\6# !\"*" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 30 "'f'(sol[2])=evalf(f(sol[2])); " }{TEXT 203 12 "valeur de f " }{TEXT 204 11 "en ce point" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#/-I\"fG6\"6#$!+Wv!\\6#!\"*$!#CF*" }{TEXT 210 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 204 "> \+ " 0 "" {TEXT 209 17 "Troisi\350me exemple" }{MPLTEXT 1 202 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> \+ " 0 "" {MPLTEXT 1 202 45 "f:=x->x^3-4*x+1;a:=0;b:=0.5;epsilon:=10^(-8) ;" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"fG6\"f* 6#I\"xGF%F%6$I)operatorGF%I&arrowGF%F%,(*$9$\"\"$\"\"\"F.!\"%F0F0F%F%F %" }{TEXT 210 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"aG6\"\"\"!" }{TEXT 210 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I\"bG6\"$\"\"&!\" \"" }{TEXT 210 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I(epsilonG6\"# \"\"\"\"*++++\"" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 31 "sol:=Dichotomie(f,a,b,epsilon);" }{TEXT 203 8 "solu tion" }{TEXT 204 36 " propos\351 par la proc\351dure Dichotomie" } {MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I$solG6\"7$\"# E$\"+**o,TD!#5" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 30 "'f'(sol[2])=evalf(f(sol[2])); " }{TEXT 203 12 "vale ur de f " }{TEXT 204 11 "en ce point" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#/-I\"fG6\"6#$\"+**o,TD!#5$!\"'!\"*" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 204 "> " 0 "" {TEXT 209 17 "Quatri\350me exemple" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 45 "f:=x->x^3-4*x+1;a:=1.5;b:=2;eps ilon:=10^(-8);" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 " 6#>I\"fG6\"f*6#I\"xGF%F%6$I)operatorGF%I&arrowGF%F%,(*$9$\"\"$\"\"\"F. !\"%F0F0F%F%F%" }{TEXT 210 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I \"aG6\"$\"#:!\"\"" }{TEXT 210 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6# >I\"bG6\"\"\"#" }{TEXT 210 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I( epsilonG6\"#\"\"\"\"*++++\"" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 31 "sol:=Dichotomie(f,a,b,epsilon);" }{TEXT 203 8 "solution" }{TEXT 204 36 " propos\351 par la proc\351dure Dichotomie" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#>I$solG6\"7$\" #E$\"+_e!3'=!\"*" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 30 "'f'(sol[2])=evalf(f(sol[2])); " }{TEXT 203 12 "vale ur de f " }{TEXT 204 11 "en ce point" }{MPLTEXT 1 202 0 "" }}{PARA 205 "" 1 "" {XPPMATH 20 "6#/-I\"fG6\"6#$\"+_e!3'=!\"*$!\"(F*" }{TEXT 210 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 211 22 "Illustration Graphique" }{TEXT 207 0 "" }}}{SECT 1 {PARA 206 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 32 "SDichotomie:=proc(f,a,b,epsilon)" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 37 "\nlocal aa,bb,compteur,milieu,suite_m;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\naa:=a;bb:=b;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 54 "\n if is(f(a)*f(b)>0) then return([infinity,infinit y]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 37 "\n elif is(f(a)=0) then return([0,a]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 37 "\n elif is(f (b)=0) then return([0,b]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\n fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\ncompteur:=1;suite_m:=N ULL;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 43 "\nmilieu:=(aa+bb)/2;sui te_m:=suite_m,milieu;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 50 "\nwhil e is(abs(bb-aa)>epsilon) and compteur " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 26 "Graphique:=proc(f,a,b,N,s)" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 32 "\nlocal i,segments,courbe,poin ts;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 29 "\nsegments:=NULL;points: =NULL;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\nfor i from 1 to N d o " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 76 "\n segments:=segments,plo t([[s[i],0],[s[i],f(s[i])]],color=blue,thickness=2);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 79 "\n points:=points,plot([[s[i],0],[s[i],0]],co lor=black,thickness=2,style=point);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 44 "\ncourbe:=plot( f,a..b,color=red,thickness=3);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\ndisplay(courbe,points,segments);" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}{PARA 207 "> " 0 "" {MPLTEXT 1 0 0 "" 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