{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 236 0 76 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 48 37 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 267 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 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0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 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 1 0 0 4 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 263 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 289 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 262 56 "Ejercicio 08-06 (del E XAMEN EXTRAORDINARIO de 22JUN11)" }}{PARA 4 "" 0 "" {TEXT -1 85 "\nCon sid\351rese la familia de m\351todos de Runge-Kutta de 3 etapas y expl \355citos de tablero" }}{PARA 4 "" 0 "" {TEXT 280 13 " 0 | " } }{PARA 4 "" 0 "" {TEXT 281 7 " " }{XPPEDIT 18 0 "alpha;" "6#%&al phaG" }{TEXT 285 8 " | " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }} {PARA 4 "" 0 "" {TEXT 284 7 " " }{XPPEDIT 18 0 "alpha;" "6#%&alp haG" }{TEXT 286 18 " | 0 " }{XPPEDIT 18 0 "alpha;" "6#%&a lphaG" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 282 25 "--- ----------------------" }}{PARA 4 "" 0 "" {TEXT 283 18 " | \+ " }{XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT 287 9 " " } {XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT 288 9 " " } {XPPEDIT 18 0 "theta;" "6#%&thetaG" }}{PARA 4 "" 0 "" {TEXT -1 66 "De \+ entre ellos se buscaran los que proporcionen el orden mas alto." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 46 "(lo que a ntecede es Ejercicio del cap\355tulo 3)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 72 "D\355gase cu\341l es la funci\363n de estabilidad de esos m\351todos de mayor orden." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y1:=f(x,y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#y1G-%\"fG6$%\"xG-%\"yG6#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y2:=subs(diff(y(x),x)=y1,diff(y1,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G,&--&%\"DG6#\"\"\"6#%\"fG6$%\"xG-%\"yG6#F/F+*&--& F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y3:=subs(diff(y(x),x)=y1,diff(y2,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y3G,*--&%\"DG6$\"\"\"F+6#%\"fG6$%\"xG-%\"yG6#F/F+*&--&F)6$F+ \"\"#F,F.F+-F-F.F+F+*&,&F4F+*&--&F)6$F8F8F,F.F+F9F+F+F+F9F+F+*&--&F)6# F8F,F.F+,&--&F)6#F+F,F.F+*&FBF+F9F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "Y1:=subs(\{y(x)=y0,x=x0\},y1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y1G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y2:=subs(\{y(x)=y0,x=x0\},y2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y2G,&--&%\"DG6#\"\"\"6#%\"fG6$%#x0G%#y0GF+*&--&F)6# \"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y3: =subs(\{y(x)=y0,x=x0\},y3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y3G, *--&%\"DG6$\"\"\"F+6#%\"fG6$%#x0G%#y0GF+*&--&F)6$F+\"\"#F,F.F+-F-F.F+F +*&,&F2F+*&--&F)6$F6F6F,F.F+F7F+F+F+F7F+F+*&--&F)6#F6F,F.F+,&--&F)6#F+ F,F.F+*&F@F+F7F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "k 1_:=f(x0,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k1_G-%\"fG6$%#x0G% #y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k2_:=f(x0+alpha*h,y 0+alpha*h*k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k2_G-%\"fG6$,&%# x0G\"\"\"*&%&alphaGF*%\"hGF*F*,&%#y0GF**(F,F*F-F*-F&6$F)F/F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k3_:=f(x0+alpha*h,y0+alpha*h *k2_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k3_G-%\"fG6$,&%#x0G\"\"\" *&%&alphaGF*%\"hGF*F*,&%#y0GF**(F,F*F-F*-F&6$F(,&F/F**(F,F*F-F*-F&6$F) F/F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k1_0:=subs(h= 0,k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k1_0G-%\"fG6$%#x0G%#y0G " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k2_0:=subs(h=0,k2_);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k2_0G-%\"fG6$%#x0G%#y0G" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_0:=subs(h=0,k3_);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k3_0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k1_,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k11G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k21G,& *&--&%\"DG6#\"\"\"6#%\"fG6$,&%#x0GF,*&%&alphaGF,%\"hGF,F,,&%#y0GF,*(F3 F,F4F,-F.6$F1F6F,F,F,F3F,F,*(--&F*6#\"\"#F-F/F,F3F,F8F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k3_,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k31G,&*&--&%\"DG6#\"\"\"6#%\"fG6$,&%#x0GF,*&%&alp haGF,%\"hGF,F,,&%#y0GF,*(F3F,F4F,-F.6$F0,&F6F,*(F3F,F4F,-F.6$F1F6F,F,F ,F,F,F3F,F,*&--&F*6#\"\"#F-F/F,,&*&F3F,F8F,F,*(F3F,F4F,,&*&-F(F9F,F3F, F,*(-F@F9F,F3F,F " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k110G \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k210G,&*&--&%\"DG6#\"\"\"6#% \"fG6$%#x0G%#y0GF,%&alphaGF,F,*(--&F*6#\"\"#F-F/F,F2F,-F.F/F,F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k310G,&*&--&%\"DG6#\"\"\"6#%\"fG6$% #x0G%#y0GF,%&alphaGF,F,*(--&F*6#\"\"#F-F/F,F2F,-F.F/F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k12G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k21,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k22G,& *&,&*&--&%\"DG6$\"\"\"F.6#%\"fG6$,&%#x0GF.*&%&alphaGF.%\"hGF.F.,&%#y0G F.*(F5F.F6F.-F06$F3F8F.F.F.F5F.F.*(--&F,6$F.\"\"#F/F1F.F5F.F:F.F.F.F5F .F.*(,&*&F=F.F5F.F.*(--&F,6$FAFAF/F1F.F5F.F:F.F.F.F5F.F:F.F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k32:=diff(k31,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k32G,(*&,&*&--&%\"DG6$\"\"\"F.6#%\"fG6$,& %#x0GF.*&%&alphaGF.%\"hGF.F.,&%#y0GF.*(F5F.F6F.-F06$F2,&F8F.*(F5F.F6F. -F06$F3F8F.F.F.F.F.F5F.F.*&--&F,6$F.\"\"#F/F1F.,&*&F5F.F:F.F.*(F5F.F6F .,&*&--&F,6#F.F/F;F.F5F.F.*(--&F,6#FEF/F;F.F5F.F>F.F.F.F.F.F.F.F5F.F.* &,&*&FAF.F5F.F.*&--&F,6$FEFEF/F1F.FFF.F.F.FFF.F.*&-FQF1F.,&*(FEF.F5F.F IF.F.*(F5F.F6F.,&*&,&*&-F*F;F.F5F.F.*(-FBF;F.F5F.F>F.F.F.F5F.F.*(,&*&F aoF.F5F.F.*(-FYF;F.F5F.F>F.F.F.F5F.F>F.F.F.F.F.F." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "k120:=subs(h=0,k12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k120G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k220G ,&*&,&*&--&%\"DG6$\"\"\"F.6#%\"fG6$%#x0G%#y0GF.%&alphaGF.F.*(--&F,6$F. \"\"#F/F1F.F4F.-F0F1F.F.F.F4F.F.*(,&*&F6F.F4F.F.*(--&F,6$F:F:F/F1F.F4F .F;F.F.F.F4F.F;F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k320 :=subs(h=0,k32);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%k320G,(*&,&*&-- &%\"DG6$\"\"\"F.6#%\"fG6$%#x0G%#y0GF.%&alphaGF.F.*(--&F,6$F.\"\"#F/F1F .F4F.-F0F1F.F.F.F4F.F.*(,&*&F6F.F4F.F.*(--&F,6$F:F:F/F1F.F4F.F;F.F.F.F 4F.F;F.F.**F:F.--&F,6#F:F/F1F.F4F.,&*&--&F,6#F.F/F1F.F4F.F.*(FEF.F4F.F ;F.F.F.F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 2 "a)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 27 "condiciones para el orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Fi_0:=expand(beta*k1_0+theta*k2_0+theta*k 3_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G,&*&%%betaG\"\"\"-%\" fG6$%#x0G%#y0GF(F(*(\"\"#F(%&thetaGF(F)F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f(x0,y0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\"\"\",&%%betaGF&*&\"\"#F &%&thetaGF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 27 "condiciones par a el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Fi10:=expan d(beta*k110+theta*k210+theta*k310);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%%Fi10G,&**\"\"#\"\"\"%&thetaGF(--&%\"DG6#F(6#%\"fG6$%#x0G%#y0GF(%&a lphaGF(F(*,F'F(F)F(--&F-6#F'F/F1F(F4F(-F0F1F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coeff(Y2,D[1](f)(x0,y0))=coeff(F i10,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\" \"\"\"\"#,$*(F(F'%&thetaGF'%&alphaGF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*coeff(coeff(Y2,D[2](f)(x0,y0)),f(x0,y0) )=coeff(coeff(Fi10,D[2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"\"\"\"#,$*(F(F'%&thetaGF'%&alphaGF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sol1:=solve(\{cond1a,cond 2a,cond2b\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol1G<%/%%betaG,& \"\"\"F)*&\"\"#F)%&thetaGF)!\"\"/%&alphaG,$*&F)F)*&\"\"%F)F,F)F-F)/F,F ," }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 2 "b)" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 258 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Fi20:=expand(beta*k120+theta*k220+theta*k320);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,,**\"\"#\"\"\"%&thetaGF(--& %\"DG6$F(F(6#%\"fG6$%#x0G%#y0GF()%&alphaGF'F(F(*,\"\"%F(F)F(--&F-6$F(F 'F/F1F(F4F(-F0F1F(F(*,F'F(F)F(F4F()F " 0 "" {MPLTEXT 1 0 76 "cond3a:=(1/6)*coeff(Y3,D[1,1 ](f)(x0,y0))=(1/2)*coeff(Fi20,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/#\"\"\"\"\"'*&%&thetaGF')%&alphaG\"\"#F'" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3b:=(1/6)*coeff(coeff( Y3,D[1,2](f)(x0,y0)),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[1,2](f)(x0,y0) ),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/#\"\"\"\"\" $,$*(\"\"#F'%&thetaGF')%&alphaGF+F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cond3c:=(1/6)*coeff(coeff(Y3,D[2,2](f)(x0,y0)),f(x0, y0)^2)=(1/2)*coeff(coeff(Fi20,D[2,2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/#\"\"\"\"\"'*&%&thetaGF')%&alphaG \"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "cond3d:=(1/6)*c oeff(coeff(Y3,D[2](f)(x0,y0)),D[1](f)(x0,y0))=(1/2)*coeff(coeff(Fi20,D [2](f)(x0,y0)),D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%' cond3dG/#\"\"\"\"\"'*&%&thetaGF')%&alphaG\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3e:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)^ 2),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)^2),f(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\"\"\"\"\"'*&%&thetaGF')%& alphaG\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "sol2:=solv e(\{cond1a,cond2a,cond2b,cond3a,cond3b,cond3c,cond3d,cond3e\},\{alpha, beta,theta\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol2G<%/%&alphaG# \"\"#\"\"$/%&thetaG#F*\"\")/%%betaG#\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 266 31 "metod o de mayor orden, orden 3," }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 268 12 " 0 | " }}{PARA 4 "" 0 "" {TEXT 269 18 " \+ 2/3 | 2/3" }}{PARA 4 "" 0 "" {TEXT 272 27 " 2/3 | 0 \+ 2/3" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 270 21 "- --------------------" }}{PARA 4 "" 0 "" {TEXT 271 36 " | \+ 1/4 3/8 3/8" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT 267 45 "que suele llamarse de NYSTR\326M de tercer orden" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 261 55 "es sabido que los m\351todos de 3 etapas y orden maximo 3" }}{PARA 0 "" 0 "" {TEXT 273 29 "tienen func i\363n de estabilidad" }}{PARA 0 "" 0 "" {TEXT 274 18 " r(z) = 1 + z + " }{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 275 1 " " } {XPPEDIT 18 0 "z^2;" "6#*$%\"zG\"\"#" }{TEXT 276 3 " + " }{XPPEDIT 18 0 "1/6;" "6#*&\"\"\"F$\"\"'!\"\"" }{TEXT 277 2 " " }{XPPEDIT 18 0 "z^ 3;" "6#*$%\"zG\"\"$" }{TEXT 278 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 265 52 "o, sea, cuatro primeros t\351rminos del desarrollo de \+ " }{XPPEDIT 18 0 "e^z;" "6#)%\"eG%\"zG" }{TEXT 279 1 " " }}}}{MARK "0 \+ 12 0" 45 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }