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{CSTYLE "" -1 341 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 342 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 343 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 344 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 345 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 346 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 347 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{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 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 Outpu t" -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 258 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 259 41 "(4) Estimaci\363n del error y cambio de paso" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 257 56 "Ejerci cio 04-04 (del EXAMEN EXTRAORDINARIO DE 15JUL09)" }}{PARA 4 "" 0 "" {TEXT -1 80 "\nSe desea construir un par encajado RK2(3) . Se quiere \+ que el m\351todo de orden 3" }}{PARA 4 "" 0 "" {TEXT -1 42 "que se uti liza sea el dado por el tablero" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 4 "" 0 "" {TEXT 256 24 " 0 | " }}{PARA 4 "" 0 "" {TEXT 264 16 " " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F $\"\"#!\"\"" }{TEXT 265 21 " | " }{XPPEDIT 18 0 "1/2 " "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 266 1 " " }}{PARA 4 "" 0 "" {TEXT 267 6 " " }{XPPEDIT 18 0 "(1+sqrt(5))/4" "6#*&,&\"\"\"F%-%%sqrtG6 #\"\"&F%F%\"\"%!\"\"" }{TEXT 268 10 " | " }{XPPEDIT 18 0 "(-3+s qrt(5))/4" "6#*&,&\"\"$!\"\"-%%sqrtG6#\"\"&\"\"\"F+\"\"%F&" }{TEXT 269 19 " 1 " }}{PARA 4 "" 0 "" {TEXT 263 1 " " }{TEXT -1 11 " ---------" }{TEXT 261 53 "----------------------------------- ------------------" }}{PARA 4 "" 0 "" {TEXT 262 30 " \+ | " }{XPPEDIT 18 0 "(-1+sqrt(5))/6" "6#*&,&\"\"\"!\"\"-%%sqr tG6#\"\"&F%F%\"\"'F&" }{TEXT 270 6 " " }{XPPEDIT 18 0 "(5-sqrt(5) )/6" "6#*&,&\"\"&\"\"\"-%%sqrtG6#F%!\"\"F&\"\"'F*" }{TEXT 271 14 " \+ " }{XPPEDIT 18 0 "1/3" "6#*&\"\"\"F$\"\"$!\"\"" }{TEXT 272 3 " " }}{PARA 4 "" 0 "" {TEXT -1 71 "B\372squese el correspondiente \+ m\351todo de orden 2 que complemente el m\351todo" }}{PARA 4 "" 0 "" {TEXT -1 57 "indicado entre los de dos o tres evaluaciones de la forma " }}{PARA 4 "" 0 "" {TEXT -1 2 " " }}{PARA 4 "" 0 "" {TEXT 260 24 " \+ 0 | " }}{PARA 4 "" 0 "" {TEXT 276 16 " \+ " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 277 21 " | " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" } {TEXT 278 1 " " }}{PARA 4 "" 0 "" {TEXT 279 6 " " }{XPPEDIT 18 0 "(1+sqrt(5))/4" "6#*&,&\"\"\"F%-%%sqrtG6#\"\"&F%F%\"\"%!\"\"" }{TEXT 280 10 " | " }{XPPEDIT 18 0 "(-3+sqrt(5))/4" "6#*&,&\"\"$!\"\"- %%sqrtG6#\"\"&\"\"\"F+\"\"%F&" }{TEXT 281 19 " 1 " }} {PARA 4 "" 0 "" {TEXT 275 1 " " }{TEXT -1 11 " ---------" }{TEXT 273 54 "------------------------------------------------------" }}{PARA 4 "" 0 "" {TEXT 274 32 " ord 2 | " }{XPPEDIT 18 0 "b[1];" "6#&%\"bG6#\"\"\"" }{TEXT 282 21 " " } {XPPEDIT 18 0 "b[2];" "6#&%\"bG6#\"\"#" }{TEXT 283 16 " \+ " }{XPPEDIT 18 0 "b[3];" "6#&%\"bG6#\"\"$" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 4 "" 0 "" {TEXT -1 56 "escribiendo el resultado en l a forma del cuadro habitual" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 284 24 " 0 | " }}{PARA 4 "" 0 "" {TEXT 292 16 " " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\" #!\"\"" }{TEXT 293 21 " | " }{XPPEDIT 18 0 "1/2" "6# *&\"\"\"F$\"\"#!\"\"" }{TEXT 294 1 " " }}{PARA 4 "" 0 "" {TEXT 295 6 " " }{XPPEDIT 18 0 "(1+sqrt(5))/4" "6#*&,&\"\"\"F%-%%sqrtG6#\"\"&F %F%\"\"%!\"\"" }{TEXT 296 10 " | " }{XPPEDIT 18 0 "(-3+sqrt(5)) /4" "6#*&,&\"\"$!\"\"-%%sqrtG6#\"\"&\"\"\"F+\"\"%F&" }{TEXT 297 19 " \+ 1 " }}{PARA 4 "" 0 "" {TEXT 287 1 " " }{TEXT -1 11 " - --------" }{TEXT 285 53 "--------------------------------------------- --------" }}{PARA 4 "" 0 "" {TEXT 286 33 " ord 2 | \+ " }{XPPEDIT 18 0 "b[1];" "6#&%\"bG6#\"\"\"" }{TEXT 301 21 " \+ " }{XPPEDIT 18 0 "b[2];" "6#&%\"bG6#\"\"#" }{TEXT 302 16 " " }{XPPEDIT 18 0 "b[3];" "6#&%\"bG6#\"\"$" }} {PARA 0 "" 0 "" {TEXT -1 11 " ---------" }{TEXT 288 56 "------------- -------------------------------------------" }}{PARA 4 "" 0 "" {TEXT 289 28 " ord 3 | " }{XPPEDIT 18 0 "(-1+sqrt(5))/6" "6#*&,&\"\"\"!\"\"-%%sqrtG6#\"\"&F%F%\"\"'F&" }{TEXT 298 6 " " } {XPPEDIT 18 0 "(5-sqrt(5))/6" "6#*&,&\"\"&\"\"\"-%%sqrtG6#F%!\"\"F&\" \"'F*" }{TEXT 299 14 " " }{XPPEDIT 18 0 "1/3" "6#*&\"\"\" F$\"\"$!\"\"" }{TEXT 300 3 " " }}{PARA 0 "" 0 "" {TEXT -1 11 " ---- -----" }{TEXT 290 57 "------------------------------------------------ ---------" }}{PARA 4 "" 0 "" {TEXT 291 31 " estim | \+ " }{XPPEDIT 18 0 "d[1];" "6#&%\"dG6#\"\"\"" }{TEXT 303 22 " \+ " }{XPPEDIT 18 0 "d[2]" "6#&%\"dG6#\"\"#" }{TEXT 304 15 " " }{XPPEDIT 18 0 "d[3]" "6#&%\"dG6#\"\"$" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 81 "y comprobando q ue el m\351todo de orden 2 obtenido es adecuado para el par encajado. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}} {EXCHG {PARA 4 "" 0 "" {TEXT -1 168 "Empezamos probando con s\363lo 2 \+ evaluaciones, ya que hay gen\351ricamente\npares encajados de esas car acter\355sticas. Como por obligaci\363n hay que formar\nun tablero de \+ la forma\n" }{TEXT 305 24 " 0 | " }}{PARA 4 "" 0 " " {TEXT 308 14 " " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\" #!\"\"" }{TEXT 309 18 " | " }{XPPEDIT 18 0 "1/2" "6#*& \"\"\"F$\"\"#!\"\"" }{TEXT 310 1 " " }}{PARA 4 "" 0 "" {TEXT 311 2 " \+ " }{TEXT -1 11 " ---------" }{TEXT 306 38 "-------------------------- ------------" }}{PARA 4 "" 0 "" {TEXT 307 31 " ord 2 | \+ " }{XPPEDIT 18 0 "b[1];" "6#&%\"bG6#\"\"\"" }{TEXT 312 21 " \+ " }{XPPEDIT 18 0 "b[2];" "6#&%\"bG6#\"\"#" }{TEXT 313 1 " " }}{PARA 4 "" 0 "" {TEXT -1 72 "y el m\351todo buscado es de \+ orden 2, o sea, consistente, necesariamente\n " }{TEXT 314 1 " " } {XPPEDIT 18 0 "b[1];" "6#&%\"bG6#\"\"\"" }{TEXT 315 3 " + " }{XPPEDIT 18 0 "b[2];" "6#&%\"bG6#\"\"#" }{TEXT 316 4 " = 1" }{TEXT -1 82 "\nlo \+ que ser\341, naturalmente, la primera condici\363n. Busquemos la neces idad de otras." }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 65 "Condiciones par a que el m\351todo sea de orden 2 y no sea de orden 3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y1:=f(x,y(x));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G-%\"fG6$%\"xG-%\"yG6#F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y2:=subs(diff(y(x),x)=y1,dif f(y1,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G,&--&%\"DG6#\"\"\"6 #%\"fG6$%\"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$\"\"\"F+6#%\"f G6$%\"xG-%\"yG6#F/F+*&--&F)6$F+\"\"#F,F.F+-F-F.F+F+*&,&F4F+*&--&F)6$F8 F8F,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 "k1_:=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+(1/2)*h,y0+(1/2)*h*k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k2_G-%\"fG6$,&%#x0G\"\"\"*&\"\"#!\"\"%\"hGF*F*,&%#y0 GF**&#F*F,F**&F.F*-F&6$F)F0F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "k3_:=f(x0+c[3]*h,y0+a[3,1]*h*k1_+a[3,2]*h*k2_);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k3_G-%\"fG6$,&%#x0G\"\"\"*&&%\"cG6# \"\"$F*%\"hGF*F*,(%#y0GF**(&%\"aG6$F/F*F*F0F*-F&6$F)F2F*F**(&F56$F/\" \"#F*F0F*-F&6$,&F)F**&F " 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#>%$k21G,&*&#\"\"\"\"\"#F(- -&%\"DG6#F(6#%\"fG6$,&%#x0GF(*&F)!\"\"%\"hGF(F(,&%#y0GF(*&F'F(*&F6F(-F 06$F3F8F(F(F(F(F(*&F'F(*&--&F-6#F)F/F1F(F;F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k3_,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k31G,&*&--&%\"DG6#\"\"\"6#%\"fG6$,&%#x0GF,*&&%\"cG6# \"\"$F,%\"hGF,F,,(%#y0GF,*(&%\"aG6$F6F,F,F7F,-F.6$F1F9F,F,*(&F<6$F6\" \"#F,F7F,-F.6$,&F1F,*&FC!\"\"F7F,F,,&F9F,*&#F,FCF,*&F7F,F>F,F,F,F,F,F, F3F,F,*&--&F*6#FCF-F/F,,(*&F;F,F>F,F,*&FAF,FDF,F,*(FAF,F7F,,&*&FKF,-F( FEF,F,*&FKF,*&-FOFEF,F>F,F,F,F,F,F,F," }}}{EXCHG {PARA 0 "> " 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:=s ubs(h=0,k21);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k210G,&*&#\"\"\"\" \"#F(--&%\"DG6#F(6#%\"fG6$%#x0G%#y0GF(F(*&F'F(*&--&F-6#F)F/F1F(-F0F1F( F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k310G,&*&--&%\"DG6#\"\"\"6#%\" fG6$%#x0G%#y0GF,&%\"cG6#\"\"$F,F,*&--&F*6#\"\"#F-F/F,,&*&&%\"aG6$F5F,F ,-F.F/F,F,*&&F?6$F5F;F,FAF,F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%$k12G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k 21,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k22G,(*&#\"\"\"\"\"%F(--& %\"DG6$F(F(6#%\"fG6$,&%#x0GF(*&\"\"#!\"\"%\"hGF(F(,&%#y0GF(*&#F(F5F(*& F7F(-F06$F3F9F(F(F(F(F(*&F'F(*&--&F-6$F(F5F/F1F(F=F(F(F(*&F;F(*&,&*&F; F(FAF(F(*&F;F(*&--&F-6$F5F5F/F1F(F=F(F(F(F(F=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$,&%#x0GF.*&&% \"cG6#\"\"$F.%\"hGF.F.,(%#y0GF.*(&%\"aG6$F8F.F.F9F.-F06$F3F;F.F.*(&F>6 $F8\"\"#F.F9F.-F06$,&F3F.*&FE!\"\"F9F.F.,&F;F.*&#F.FEF.*&F9F.F@F.F.F.F .F.F.F5F.F.*&--&F,6$F.FEF/F1F.,(*&F=F.F@F.F.*&FCF.FFF.F.*(FCF.F9F.,&*& FMF.--&F,6#F.F/FGF.F.*&FMF.*&--&F,6#FEF/FGF.F@F.F.F.F.F.F.F.F.F5F.F.*& ,&*&FPF.F5F.F.*&--&F,6$FEFEF/F1F.FTF.F.F.FTF.F.*&-F[oF1F.,&*(FEF.FCF.F XF.F.*(FCF.F9F.,(*&#F.\"\"%F.-F*FGF.F.*&F]pF.*&-FQFGF.F@F.F.F.*&FMF.*& ,&*&FMF.FbpF.F.*&FMF.*&-FcoFGF.F@F.F.F.F.F@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,(*&#\"\"\"\"\"%F(--&%\"DG6$F(F(6#%\"fG6$%#x0G%#y0GF(F(*&F' F(*&--&F-6$F(\"\"#F/F1F(-F0F1F(F(F(*&#F(F:F(*&,&*&F=F(F6F(F(*&F=F(*&-- &F-6$F:F:F/F1F(F;F(F(F(F(F;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.&%\"cG6#\"\" $F.F.*&--&F,6$F.\"\"#F/F1F.,&*&&%\"aG6$F7F.F.-F0F1F.F.*&&FA6$F7F=F.FCF .F.F.F.F.F4F.F.*&,&*&F9F.F4F.F.*&--&F,6$F=F=F/F1F.F>F.F.F.F>F.F.**F=F. --&F,6#F=F/F1F.FEF.,&*&#F.F=F.--&F,6#F.F/F1F.F.*&FVF.*&FPF.FCF.F.F.F.F ." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 317 27 "condiciones para el orden 1 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Fi_0:=expand(b[1]*k1_0+ b[2]*k2_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G,&*&&%\"bG6#\" \"\"F*-%\"fG6$%#x0G%#y0GF*F**&&F(6#\"\"#F*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/\"\"\",&&%\"bG6#F&F& &F)6#\"\"#F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 318 27 "condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Fi10:=expand (b[1]*k110+b[2]*k210);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10G,&*& #\"\"\"\"\"#F(*&&%\"bG6#F)F(--&%\"DG6#F(6#%\"fG6$%#x0G%#y0GF(F(F(*&F'F (*(F+F(--&F1F-F3F5F(-F4F5F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coeff(Y2,D[1](f)(x0,y0))=coeff(Fi10,D[1](f)(x0,y 0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\"\"\"#,$*&F&F '&%\"bG6#F(F'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/#\" \"\"\"\"#,$*&F&F'&%\"bG6#F(F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "soluciones:=solve(\{cond1a,cond2a,cond2b\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+solucionesG<$/&%\"bG6#\"\"\"\"\"!/&F(6#\"\"#F*" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 319 81 "o sea, esto nos obliga a que el m\351todo de orden 2, de entre los de 2 evaluaciones" }}{PARA 0 "" 0 "" {TEXT 320 40 "buscados sea el m\351todo 'del punto medio'" }}{PARA 4 "" 0 "" {TEXT 322 13 " 0 | " }}{PARA 4 "" 0 "" {TEXT 323 6 " " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 326 8 " \+ | " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 327 2 " \+ " }}{PARA 4 "" 0 "" {TEXT -1 13 " ---------" }{TEXT 324 11 "------- ----" }}{PARA 4 "" 0 "" {TEXT 325 26 " | 0 1" }} {PARA 0 "" 0 "" {TEXT 321 75 "comprobaremos que este m\351todo es uno \+ de los adecuados para el par encajado " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "b[1]:=0;b[2]:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> &%\"bG6#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"# \"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 328 75 "condiciones para el or den 3 y coeficientes del t\351rminio principal del error" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Fi20:=expand(b[1]*k120+b[2]*k220); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,(*&#\"\"\"\"\"%F(--&%\"DG 6$F(F(6#%\"fG6$%#x0G%#y0GF(F(*&#F(\"\"#F(*&--&F-6$F(F6F/F1F(-F0F1F(F(F (*&F'F(*&--&F-6$F6F6F/F1F()F " 0 "" {MPLTEXT 1 0 153 "cond3a:=(1/6)*coeff(Y3,D[1,1](f)(x0,y0))=(1/2)*coeff (Fi20,D[1,1](f)(x0,y0));\ncoef3a:=(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/#\"\"\"\"\"'#F'\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'co ef3aG#\"\"\"\"#C" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 217 "cond3b :=(1/6)*coeff(coeff(Y3,D[1,2](f)(x0,y0)),f(x0,y0))=(1/2)*coeff(coeff(F i20,D[1,2](f)(x0,y0)),f(x0,y0));\ncoef3b:=(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/#\"\"\"\"\"$#F'\"\"% " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'coef3bG#\"\"\"\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 225 "cond3c:=(1/6)*coeff(coeff(Y3,D[2,2 ](f)(x0,y0)),f(x0,y0)^2)=(1/2)*coeff(coeff(Fi20,D[2,2](f)(x0,y0)),f(x0 ,y0)^2);\ncoef3c:=(1/6)*coeff(coeff(Y3,D[2,2](f)(x0,y0)),f(x0,y0)^2)-( 1/2)*coeff(coeff(Fi20,D[2,2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/#\"\"\"\"\"'#F'\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'coef3cG#\"\"\"\"#C" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 233 "cond3d:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)),D[1](f) (x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)),D[1](f)(x0,y0));\ncoef 3d:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)),D[1](f)(x0,y0))-(1/2)*coeff(c oeff(Fi20,D[2](f)(x0,y0)),D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/#\"\"\"\"\"'\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'coef3dG#\"\"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 217 "cond3e:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)^2),f(x0, y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)^2),f(x0,y0));\ncoef3e:=(1/6 )*coeff(coeff(Y3,D[2](f)(x0,y0)^2),f(x0,y0))-(1/2)*coeff(coeff(Fi20,D[ 2](f)(x0,y0)^2),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3 eG/#\"\"\"\"\"'\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'coef3eG#\" \"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 58 "Lo que es razonable, por lo que se obtien e el par encajado" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 329 24 " 0 | " }}{PARA 4 "" 0 "" {TEXT 337 16 " " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" } {TEXT 338 21 " | " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F $\"\"#!\"\"" }{TEXT 339 1 " " }}{PARA 4 "" 0 "" {TEXT 340 6 " " } {XPPEDIT 18 0 "(1+sqrt(5))/4" "6#*&,&\"\"\"F%-%%sqrtG6#\"\"&F%F%\"\"%! \"\"" }{TEXT 341 10 " | " }{XPPEDIT 18 0 "(-3+sqrt(5))/4" "6#*& ,&\"\"$!\"\"-%%sqrtG6#\"\"&\"\"\"F+\"\"%F&" }{TEXT 342 19 " \+ 1 " }}{PARA 4 "" 0 "" {TEXT 332 1 " " }{TEXT -1 11 " --------- " }{TEXT 330 53 "----------------------------------------------------- " }}{PARA 4 "" 0 "" {TEXT 331 75 " ord 2 | \+ 0 1 0" }}{PARA 0 "" 0 "" {TEXT -1 11 " ---------" }{TEXT 333 56 "-------------------------------------- ------------------" }}{PARA 4 "" 0 "" {TEXT 334 28 " ord 3 \+ | " }{XPPEDIT 18 0 "(-1+sqrt(5))/6" "6#*&,&\"\"\"!\"\"-%%sqrtG 6#\"\"&F%F%\"\"'F&" }{TEXT 343 6 " " }{XPPEDIT 18 0 "(5-sqrt(5))/ 6" "6#*&,&\"\"&\"\"\"-%%sqrtG6#F%!\"\"F&\"\"'F*" }{TEXT 344 14 " \+ " }{XPPEDIT 18 0 "1/3" "6#*&\"\"\"F$\"\"$!\"\"" }{TEXT 345 3 " " }}{PARA 0 "" 0 "" {TEXT -1 11 " ---------" }{TEXT 335 57 "------ ---------------------------------------------------" }}{PARA 4 "" 0 " " {TEXT 336 28 " estim | " }{XPPEDIT 18 0 "(-1+sqrt (5))/6" "6#*&,&\"\"\"!\"\"-%%sqrtG6#\"\"&F%F%\"\"'F&" }{TEXT 346 8 " \+ " }{XPPEDIT 18 0 "(-1-sqrt(5))/6" "6#*&,&\"\"\"!\"\"-%%sqrtG6#\" \"&F&F%\"\"'F&" }{TEXT 347 9 " " }{XPPEDIT 18 0 "1/3" "6#*&\" \"\"F$\"\"$!\"\"" }}}}{MARK "0 3 0" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }