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Il a comme but d'initier l'\351tudiant \340 quelques commandes \+ Maple, comme solve et subs, et \340 des trac\351s de graphiques, utile s par la suite." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart: " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 291 51 "Principales commandes utili s\351es dans ce laboratoire" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "sol ve, evalf, fsolve, subs, rhs, lhs, allvalues, assign, unassign, numer " }}{PARA 0 "" 0 "" {TEXT -1 65 "Avec les graphiques : plot, implicitp lot, disk, textplot, display" }}{PARA 0 "" 0 "" {TEXT -1 78 "Note : S \351lectionner un mot et utiliser l'aide de Maple pour plus d'informat ion" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 256 47 "La commande solve et re pr\351sentations graphiques" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Sol ution d'un syst\350me d'\351quations avec : " }}{PARA 256 "" 0 "" {TEXT -1 75 "solve(\{\351quation1,\351quation2...\351quationn\},\{vari able1,variable2,..variablep\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 285 11 "Exemple 1 :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "solve(\{ 3*x-4*y=8,12*x+2*y=12\},\{x,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 116 "La solution repr\351sente le point d'intersection des 2 droites 3 *x - 4*y = 8 et 12*x + 2*y =12. Tra\347ons le graphique :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "with(plots): #biblioth\350que(pack age) n\351cessaire pour tracer le graphique\nimplicitplot(\{3*x-4*y=8, 12*x+2*y=12\},x=-3..3,y=-3..3);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "On peut ajouter des options au graphique : " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 293 "p:=pointplot([32/27,-10/9], color=black):#place un point \340 l'intersection des droites \ntextes: =textplot(\{[1.3,-1.3,`intersection`],[2.3,-0.7,`3x-4y=8`],[1.1,2,`12x +2y=12`]\}):\ndroites:=implicitplot(\{3*x-4*y=8,12*x+2*y=12\},x=-3..3, y=-3..3):\ndisplay(p,droites,textes,title='droites_concourantes');" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "Au lieu de la commande pointplot \+ , on peut utiliser disk. Voir exemple 6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 286 11 "Exemple 2 :" }{TEXT -1 79 " Dans le cas o\371 il n'y a q u'une seule \351quation, on peut omettre les accolades. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " solve(3*x^3-13*x^2+9*x+10=0,x);" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Pour convertir des nombres en vi rgule flottante (en d\351cimales)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Le g raphique de 3*x^3-13*x^2+9*x+10 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot(3*x^3-13*x^2+9*x+10,x=-2..5,y=-5..15);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Si on veut les r\351ponses en virg ule flottante (d\351cimales), on utilise " }{TEXT 284 28 "fsolve(\351q uations, variables)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "fsol ve(3*x^3-13*x^2+9*x+10=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 287 11 " Exemple 3 :" }{TEXT -1 165 " fsolve peut ne donner qu'un seul z\351ro , en particulier lorsque les \351quations ne sont pas polynomiales. Ce pendant, on peut lui pr\351ciser sur quel intervalle chercher." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "q := sin(cos(x));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "fsolve(q=0,x);# ou fsolve(q, x)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(q,x=-6..6);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "fsolve(q=0, x,4..6);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 295 11 "Exemple 4 :" }{TEXT -1 95 " Trouv er les points d'intersections des courbes : y = 2x^3 - 3x^2 - 11x + 6 \+ et y = x^3 - 7x - 6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "eq1 \+ := y = 2*x^3-3*x^2-11*x+6;\neq2 := y = x^3-7*x-6;" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 42 "Pour extraire le membre de droite de eq1: " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "rhs(eq1);#rhs:right hand sid e, lhs:left hand side" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "so lve(eq1,y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(rhs(eq 1)=rhs(eq2),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(\{r hs(eq1),rhs(eq2)\},x=-2.5..3.5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 260 "" 0 "" {TEXT 257 69 "Solutions avec solve de syst\350me d' \351quations lin\351aires avec param\350tres" }{TEXT -1 2 ". " }} {EXCHG {PARA 0 "" 0 "" {TEXT 288 11 "Exemple 5 :" }{TEXT -1 145 " Pour quelles valeurs de a et b, le syst\350me d'\351quations suivant a-t-i l \na) une solution unique? b) une infinit\351 de solutions? c) pas de solution?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "eq3:=b*x+7*y- 3*z=12;eq4:=-2*x+5*y+4*z=-5;eq5:=30*x-22*y-35*z = a;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solve(\{eq3,eq4,eq5\},\{x,y,z\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "a) " }{TEXT 260 81 "Le syst\350me a une solution unique si b < > 668/87. \" < >\" signifie \"diff\351rent de\"" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 3 "b) " }{TEXT 264 46 "Le syst\350me n'a pa s de solution si b = 668/87." }{TEXT 293 1 " " }{TEXT 265 4 "FAUX" } {TEXT 266 69 " : Si les 3 num\351rateurs s'annulent en m\352me temps q ue le d\351nominateur," }{TEXT -1 83 " c'est qu'on a un syst\350me d' \351quations \351quivalent \340 : 0x = 0, 0y = 0, 0z = 0 qui a " } {TEXT 261 25 "une infinit\351 de solutions" }{TEXT -1 2 ": " }}} {EXCHG {PARA 0 "" 0 "" {TEXT 268 12 "Attention : " }{TEXT 267 6 "Maple " }{TEXT 269 9 "consid\350re" }{TEXT 270 79 " tout param\350tre ou to ute expression contenant des param\350tres comme \351tant <> 0. " } {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 292 30 "Explication (cl iquez sur le +)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 379 " L'\351quation lin\351aire du premier degr\351, ax = b, Maple donne comme solution u nique x = b / a sans s'occuper des possibilit\351s de division par 0 ( si a = 0) car le param\350tre a n'a pas de valeur d\351finie. \nSi a = 0 et b = 0 le syst\350me initial est 0x = 0 qui a une infinit\351 de \+ solutions. \311videmment, le syst\350me n'a pas de solution si a = 0 \+ et b <> 0 et une solution unique si a <> 0. " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "x=solve(a*x=b,x);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 52 "#Autre exemple: \nsolve(\{3*x+4*y=c,3*x+4*y=d\},\{x ,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 224 "Les 2 \351quations 3*x +4*y = c et 3*x+4*y = d n'ont pas de solution si c<>d mais ont une inf init\351 de solutions si c = d. Maple, en ne r\351pondant rien, indiq ue que les \351quations 3*x+4*y = c et 3*x+4*y = d n'ont pas de soluti on. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 " " {TEXT -1 80 "Si Maple indique qu'un syst\350me d'\351quations avec p aram\350tres n'a pas de solution, " }{TEXT 294 88 "on doit analyser la situation, en particulier, dans les cas o\371 un d\351nominateur s'an nule." }{TEXT -1 239 " Par exemple, si Maple donne une solution de la \+ forme, x = b/a, y = c/a, il faut analyser le cas o\371 a = 0. On pourr a avoir une infinit\351 de solutions si on trouve b = 0 et c = 0 (les \+ num\351rateurs s'annulent en m\352me temps que le d\351nominateur)" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 "Le d\351nominateur s'annule \340 \+ b = 668/87 et alors les num\351rateurs s'annulent-ils en m\352me temps ?" }}{PARA 0 "" 0 "" {TEXT -1 50 "Substituons b = 668/87 dans les 3 n um\351rateurs avec" }}{PARA 0 "" 0 "" {TEXT -1 12 "la commande " } {TEXT 282 64 "subs(\{x1=a1,x2=a2,...xn=an\},\{\351quation1,\351quation 2,...,\351quationk\})" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "su bs(b=668/87,\{-175*b+4*b*a-150-6*a=0,-110*b+5*b*a-2322+14*a=0,-2599+43 *a=0\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(%,a);" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Les num\351rateurs s'annulent tou s pour a = 2599/43 lorsque b = 668/87" }}{PARA 0 "" 0 "" {TEXT 258 81 "Le syst\350me a une infinit\351 de solutions si b = 668/87 et a = 259 9/43. V\351rifions : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "su bs(\{a=2599/43,b=668/87\},\{eq3,eq4,eq5\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(%,\{x,y,z\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 204 "Quand Maple donne, variable = variable, dans une solutio n, cela signifie qu'on peut donner \340 \"variable\" n'importe quelle \+ valeur, On a une infinit\351 de solutions. On appelle \"variable\", u ne variable libre." }}{PARA 0 "" 0 "" {TEXT -1 61 "Ici, on a une varia ble libre, donc une infinit\351 de solutions " }{TEXT 262 30 "si b = 6 68/87 et a = 2599/43. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 68 "c) Le \+ syst\350me n'a pas de solutions si b = 668/87 et a <> 2599/43 " }}} {PARA 0 "" 0 "" {TEXT -1 24 "Note : Pour \351tudier les " }{TEXT 278 1 "s" }{TEXT -1 30 "yst\350mes d'\351quations lin\351aires " }{TEXT 279 50 "avec param\350tres, la m\351thode d'\351limination de Gauss" } {TEXT -1 26 " (gausselim sans backsub) " }{TEXT 263 15 "est pr\351f \351rable," }{TEXT -1 76 " en g\351n\351ral, aux autres m\351thodes. V oir le laboratoire 6 et le compl\351ment 6b." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 259 "" 0 "" {TEXT 280 20 "Cas o \371 Maple r\351pond " }{TEXT 271 17 "RootOF(expression" }{TEXT 281 1 ")" }}{EXCHG {PARA 0 "" 0 "" {TEXT 275 18 "RootOF(expression)" }{TEXT -1 56 " garde en m\351moire les z\351ros (racines) de expression = 0. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 289 11 "Exemple 6 :" }{TEXT -1 107 " Trouver, s'ils existent les points d'intersections du cercle 2x^2+2y ^2+6x-3y=5 et de la droite 4*x+5*y=5." }{TEXT 274 1 " " }{TEXT -1 1 ": " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "eq1:=2*x^2+2*y^2+6*x-3*y=5;eq2:=4* x+5*y=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "implicitplot(\{ eq1,eq2\},x=-5..5,y=-5..5); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(\{eq1,eq2\},\{x,y\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "allvalues(%); # donne toutes les valeurs de Roo tOf()" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Repr\351sentons ces points sur un \+ graphique avec pointplot ou disk " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "with(plottools):graphe:=implicitplot(\{eq1,eq2\},x=- 5..5,y=-5..5): intersection1:=disk([-2.360360992,2.888288793],0.1,colo r=blue):\nintersection2:=disk([.7749951382,.380003889],0.1,color=blue) :\ndisplay(graphe,intersection1,intersection2);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 172 "intersection3:=pointplot([-2.360360992,2.8882 88793],color=blue):\nintersection4:=pointplot([.7749951382,.380003889] ,color=blue):\ndisplay(graphe,intersection3,intersection4);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Une autre approche en utilisant fs olve " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "fsolve(\{eq1,eq2\} ,\{x,y\}); # fsolve ne donne qu'une des 2 solutions " }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Trouvons l'autre point d'intersect ion :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "fsolve(\{eq1,eq2\} ,\{x,y\},x=-4..-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 290 11 "Exemple 7 :" }{TEXT 273 35 " Inte rpr\351tation des solutions Maple" }{TEXT -1 163 " : Maple indique les valeurs des variables qui sont solutions mais ne donne pas ces valeur s \340 ces variables : pour assigner les valeurs aux variables, on ut ilise " }{TEXT 272 6 "assign" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "sol:=solve(\{x-y=12,7*x+67*y=2\},\{x,y\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x;y;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "x et y n'ont pas de valeurs. Donnons x et y leurs valeurs dans sol ave c assign(sol);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign(so l);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Pour effacer des valeurs, on utilise unassign \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "unassign('x','y');# On \+ peut aussi utiliser x:='x':y:='y': " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT 276 9 "Exercices" }{TEXT -1 1 " " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 302 5 "No 1)" }{TEXT 303 1 " " }{TEXT -1 56 "R\351soudre, avec solve, le syst\350me d'\351quations lin\351aires :" }}{PARA 0 " " 0 "" {TEXT -1 53 " 2x1 - 6x2 + 3x3 - 2x4 = 5\n -x1 + 3x2 - 2x3 \+ = 4" }}{PARA 0 "" 0 "" {TEXT -1 35 " 3x1 - 9x2 + 4x3 - 4x4 = 14 \+ " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 277 32 " Espace de travail de l' \351tudiant" }}{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 "" {TEXT -1 0 "" }{TEXT 304 5 "No 2)" }{TEXT -1 68 " Soit 2*x^2 + 2*y^2 + x*y + 6*x - 3*y = 5 et \+ x^2 + 4*x + 5*y = 5 \n" }{TEXT 305 2 "a)" }{TEXT -1 40 " Tracer sur u n graphique ces 2 coniques " }}{PARA 0 "" 0 "" {TEXT 306 2 "b)" } {TEXT -1 49 " Trouver, avec fsolve, les points d'intersections" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT 296 31 "Espace de travail de l'\351tudia nt" }}{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 "" {TEXT -1 56 "Soit A(-3,7), B(2,5), C(5,-7 ) et D(8,12) quatre points. " }}{PARA 0 "" 0 "" {TEXT 308 2 "a)" } {TEXT -1 38 " Trouver a,b,c,d pour que la courbe de" }{TEXT 307 29 " y = a*x^3 + b*x^2 + c*x + d." }{TEXT -1 37 " passe par les 4 points A, \+ B, C et D." }}{PARA 0 "" 0 "" {TEXT 309 2 "b)" }{TEXT -1 35 " Tracer l a courbe avec les 4 points" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 297 31 "E space de travail de l'\351tudiant" }}{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 "" {TEXT 310 5 "No 4)" }{TEXT -1 74 " Pour quelles valeurs de a et b, le \+ syst\350me d'\351quations suivant a-t-il : \n" }{TEXT 311 2 "a)" } {TEXT -1 23 " une solution unique ?\n" }{TEXT 312 2 "b)" }{TEXT -1 19 " pas de solution ?\n" }{TEXT 313 2 "c)" }{TEXT -1 29 " une infinit \351 de solutions ?\n" }{XPPEDIT 18 0 "10*x+27*y+27*z = 4;" "6#/,(*&\" #5\"\"\"%\"xGF'F'*&\"#FF'%\"yGF'F'*&F*F'%\"zGF'F'\"\"%" }{TEXT -1 1 " \n" }{XPPEDIT 18 0 "2*x-120*y+383*z = b;" "6#/,(*&\"\"#\"\"\"%\"xGF'F' *&\"$?\"F'%\"yGF'!\"\"*&\"$$QF'%\"zGF'F'%\"bG" }{TEXT -1 1 "\n" } {XPPEDIT 18 0 "32*x-48*y+200*z = a;" "6#/,(*&\"#K\"\"\"%\"xGF'F'*&\"#[ F'%\"yGF'!\"\"*&\"$+#F'%\"zGF'F'%\"aG" }{TEXT -1 1 "\n" }{XPPEDIT 18 0 "12*x+534*y-1478*z = 8-4*b;" "6#/,(*&\"#7\"\"\"%\"xGF'F'*&\"$M&F'%\" yGF'F'*&\"%y9F'%\"zGF'!\"\",&\"\")F'*&\"\"%F'%\"bGF'F/" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 299 32 " Espace de travail de l'\351tudiant" }} {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 "" {TEXT 314 4 "No 5" }{TEXT 315 1 ")" }{TEXT -1 21 " m\352me question que 4)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {XPPEDIT 18 0 "37*x+19*y+5*z = 4;" "6#/,(*&\"#P\"\"\"%\"xGF'F'*&\"#>F' %\"yGF'F'*&\"\"&F'%\"zGF'F'\"\"%" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{XPPEDIT 18 0 "13*x-12*y+4*z = b;" "6#/,(*&\"#8\"\"\"% \"xGF'F'*&\"#7F'%\"yGF'!\"\"*&\"\"%F'%\"zGF'F'%\"bG" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }{XPPEDIT 18 0 "7*x+3*y+a*z = 12;" "6#/,(*&\"\"(\"\"\" %\"xGF'F'*&\"\"$F'%\"yGF'F'*&%\"aGF'%\"zGF'F'\"#7" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 300 31 "Espace de travail de l'\351tudiant" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {EXCHG {PARA 0 "" 0 "" {TEXT 318 5 "No 6)" }{TEXT -1 18 " (Optionnel) \+ Soit " }{XPPEDIT 18 0 "y = a*exp(x)+b*exp(2*x)+c*exp(3*x);" "6#/%\"yG, (*&%\"aG\"\"\"-%$expG6#%\"xGF(F(*&%\"bGF(-F*6#*&\"\"#F(F,F(F(F(*&%\"cG F(-F*6#*&\"\"$F(F,F(F(F(" }{TEXT -1 57 "\nTrouver a,b,c si y(0) = 1, y '(0) = 5 et y ''(0) = 11 . " }}{PARA 0 "" 0 "" {TEXT -1 5 "Note " } {XPPEDIT 18 0 "exp(x)" "6#-%$expG6#%\"xG" }{TEXT -1 87 " s'\351crit, d ans Maple, exp(x), y '(0) = 5 signifie : \340 x = 0 , y ' = dy/dx = 5 \nNote : " }{TEXT 316 22 " diff(f(x),x) = dy/dx " }{TEXT -1 3 "et " } {TEXT 317 15 "diff(f(x),x$n) " }{TEXT -1 36 "repr\351sente la d\351riv \351e n i\350me de f(x)" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 301 32 " Esp ace de travail de l'\351tudiant" }}{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 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }