{VERSION 3 0 "IBM INTEL LINUX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 256 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Ou tput" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } } {SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 27 "Problema #4 (Interpolaci\363n) " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "\"Dada la funci\363n " } {XPPEDIT 18 0 "f(x) = e^x;" "6#/-%\"fG6#%\"xG)%\"eGF'" }{TEXT -1 16 "e n el intervalo " }{XPPEDIT 18 0 "[0, 2];" "6#7$\"\"!\"\"#" }{TEXT -1 31 " se pide aproximar su valor en " }{XPPEDIT 18 0 "x = .25;" "6#/%\" xG$\"#D!\"#" }{TEXT -1 46 " usando interpolaci\363n lineal con los sop ortes:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 " (a) " }{XPPEDIT 18 0 "x[0] = 0,x[1] = .5;" "6$/&%\"xG6#\"\"!F'/&F%6# \"\"\"$\"\"&!\"\"" }{TEXT -1 1 "," }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 4 "(b) " }{XPPEDIT 18 0 "x[0] = .5,x[1] = 1; " "6$/&%\"xG6#\"\"!$\"\"&!\"\"/&F%6#\"\"\"\"\"\"" }{TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "(c) " } {XPPEDIT 18 0 "x[0] = 0,x[1] = 1,x[2] = 2;" "6%/&%\"xG6#\"\"!F'/&F%6# \"\"\"\"\"\"/&F%6#\"\"#\"\"#" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Comparar y comentar los r esultados anteriores\"." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 9 "Soluci\363n:" }}{PARA 0 "" 0 "" {TEXT -1 103 "En to dos los casos se puede proceder definiendo directamente el polinomio d e interpolaci\363n como sigue:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 4 "(a):" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 61 "p:=proc(x::uneval) interp([0, .5], [exp(0), \+ exp(.5)], x) end;" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pGR6#'%\"xG%'unevalG6\"F*F*-%'inte rpG6%7$\"\"!$\"\"&!\"\"7$-%$expG6#F/-F56#F09$F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "p(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#, &%\"xG$\"+UDW(H\"!\"*\"\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "z:=evalf(p(y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,&%\"yG $\"+UDW(H\"!\"*$\"\"\"\"\"!F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "y:=.25;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG$\"#D!\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(z);" }{TEXT -1 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+O1OC8!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "El error cometido en la aproximacion es" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "abs(z-exp(.25));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\")>_LS!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Dibujamos la funci\363n y su polinomio de interpolac i\363n:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot([p(x),exp(x)], x=-1..1);" }}{PARA 13 "" 1 "" {INLPLOT "6& -%'CURVESG6$7S7$$!\"\"\"\"!$!1+++?aUuH!#;7$$!1nmm;p0k&*F-$!1#o#zF-7$$!1nmmT%p\"e()F-$!1?FmB;Aj8F-7$$!1 mmm\"4m(G$)F-$!1JS&p\\a41)!#<7$$!1ML$3i.9!zF-$!1Q+#=*><;DFB7$$!1nm;/R= 0vF-$\"1_^+s6bCEFB7$$!1++]P8#\\4(F-$\"1/'ReCsu%zFB7$$!1nm;/siqmF-$\"1Z ;\\$[W_M\"F-7$$!1++](y$pZiF-$\"1\"R32HwR*=F-7$$!1LLL$yaE\"eF-$\"1UN9-W TeCF-7$$!1nmm\">s%HaF-$\"1*oDzzrb&HF-7$$!1+++]$*4)*\\F-$\"1^u;uKD:NF-7 $$!1+++]_&\\c%F-$\"1bPKcGBxSF-7$$!1+++]1aZTF-$\"1oc,;V!)=YF-7$$!1nm;/# 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\"\"F*$\"1+++UDW(H#Fgs-%'COLOURG6&%$RGBG$\"#5F)F*F*-F$6$7S7$F($\"1BWr6 WzyOF-7$F/$\"1W^QtfrUQF-7$F4$\"1%*)f+Ru7*RF-7$F9$\"1cu^dg@lTF-7$F>$\"1 'GlMXnzM%F-7$FD$\"1d)=:(4\"y`%F-7$FI$\"14;0fu@@ZF-7$FN$\"1E.r.&R*=\\F- 7$FS$\"1y!*=&=Q@8&F-7$FX$\"1m09a)[QN&F-7$Fgn$\"1q7XaF!>f&F-7$F\\o$\"11 uvRHL5eF-7$Fao$\"1h`=4&fk1'F-7$Ffo$\"1o)*)HW)*\\L'F-7$F[p$\"1Sdj9q-0mF -7$F`p$\"1d1T#y(>goF-7$Fep$\"16<*Q)=[wrF-7$Fjp$\"1!y\\.E)zbuF-7$F_q$\" 1wFu%Q;Wz(F-7$Fdq$\"18-HV,'p5)F-7$Fiq$\"1.F]goIk%)F-7$F^r$\"1.[k;i@>)) F-7$Fcr$\"1ad-&\\+a?*F-7$Fhr$\"1i#G[g:\\d*F-7$F]s$\"1%)QMzI8!***F-7$Fc s$\"1Z0q6.0W5Fgs7$Fis$\"1t^ka\\!\\3\"Fgs7$F^t$\"1(zM@lE38\"Fgs7$Fct$\" 1$e]g`5.=\"Fgs7$Fht$\"1E;`;c\"3B\"Fgs7$F]u$\"1&y'4$)zt\"G\"Fgs7$Fbu$\" 1'>'[,1vS8Fgs7$Fgu$\"1+#pi+!4'R\"Fgs7$F\\v$\"1IAQE.qd9Fgs7$Fav$\"1!Rtq Mte^\"Fgs7$Ffv$\"1E+V%\\J@e\"Fgs7$F[w$\"1]tZ?v6Z;Fgs7$F`w$\"1%f'fjFgs7 $Fdx$\"1vSfBwPK?Fgs7$Fix$\"1J]$\\l(p>@Fgs7$F^y$\"1i!=R[RK?#Fgs7$Fcy$\" 1=Ad$*[/.BFgs7$Fhy$\"1`]xri8'R#Fgs7$F]z$\"1WqM`&R&*\\#Fgs7$Fbz$\"1sQsf lo-EFgs7$Fgz$\"1X!f%G=G=FFgs-F\\[l6&F^[lF*F_[lF*-%+AXESLABELSG6$Q\"x6 \"%!G-%%VIEWG6$;F(Fgz%(DEFAULTG" 2 267 267 267 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 4496 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Con el s iguiente soporte," }}{PARA 0 "" 0 "" {TEXT -1 4 "(b):" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 63 "p:=proc(x::uneval) interp([0.5, 1], [exp(0.5 ), exp(1)], x) end;" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pGR6#'%\"xG%'unevalG6\"F*F*-%'inte rpG6%7$$\"\"&!\"\"\"\"\"7$-%$expG6#F/-F56#F29$F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(p(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG$\"+967R@!\"*$\"*92;z&F'\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "z:=evalf(p(y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,&%\"yG$\"+967R@!\"*$\"*92;z&F)\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "y:=.25;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG$\"#D!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+$*4%R6\"!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "El error cometido en la aproxim aci\363n es" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "abs(z-exp(.25));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*CW3q\" !\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "De nuevo comparamos las g r\341ficas de la funci\363n y su polinomio de interpolaci\363n:" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot([p (x),exp(x)],x=-1..1);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7S7$ $!\"\"\"\"!$!1NrP,/'*f:!#:7$$!1nmm;p0k&*!#;$!1_5$f*oqm9F-7$$!1LL$3m%>vc&Q\"F-7$$!1nmmT%p\"e()F1$!1+!HX!yJ%H\"F-7$$!1mmm\"4m(G$)F 1$!1V)[sAjC?\"F-7$$!1ML$3i.9!zF1$!1G0u=_/66F-7$$!1nm;/R=0vF1$!1wO`A!*G E5F-7$$!1++]P8#\\4(F1$!1&f>j!*)G&Q*F17$$!1nm;/siqmF1$!1&RqnOswZ)F17$$! 1++](y$pZiF1$!1oU(\\cmHd(F17$$!1LLL$yaE\"eF1$!1:%[`WlBk'F17$$!1nmm\">s 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$F\\o$\"11uvRHL5eF17$Fao$\"1h`=4&fk1'F17$Ffo$\"1o)*)HW)*\\L'F17$F[p$\" 1Sdj9q-0mF17$F`p$\"1d1T#y(>goF17$Fep$\"16<*Q)=[wrF17$Fjp$\"1!y\\.E)zbu F17$F`q$\"1wFu%Q;Wz(F17$Feq$\"18-HV,'p5)F17$Fjq$\"1.F]goIk%)F17$F_r$\" 1.[k;i@>))F17$Fdr$\"1ad-&\\+a?*F17$Fir$\"1i#G[g:\\d*F17$F^s$\"1%)QMzI8 !***F17$Fds$\"1Z0q6.0W5F-7$Fis$\"1t^ka\\!\\3\"F-7$F^t$\"1(zM@lE38\"F-7 $Fct$\"1$e]g`5.=\"F-7$Fht$\"1E;`;c\"3B\"F-7$F]u$\"1&y'4$)zt\"G\"F-7$Fb u$\"1'>'[,1vS8F-7$Fgu$\"1+#pi+!4'R\"F-7$F\\v$\"1IAQE.qd9F-7$Fav$\"1!Rt qMte^\"F-7$Ffv$\"1E+V%\\J@e\"F-7$F[w$\"1]tZ?v6Z;F-7$F`w$\"1%f'fjF-7$Fdx$ \"1vSfBwPK?F-7$Fix$\"1J]$\\l(p>@F-7$F^y$\"1i!=R[RK?#F-7$Fcy$\"1=Ad$*[/ .BF-7$Fhy$\"1`]xri8'R#F-7$F]z$\"1WqM`&R&*\\#F-7$Fbz$\"1sQsflo-EF-Ffz-F \\[l6&F^[lF*F_[lF*-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F(Fgz%(DEFAULTG " 2 267 267 267 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 459 "La situaci\363n ha empeorado. Obs\351rvese que , en el primer caso, el punto cuya imagen se quer\355a aproximar esta \+ entre los puntos del soporte, mientras que en el segundo caso el punto esta situado a la izquierda del soporte. Cuando ocurre esto, se dice \+ que se est\341 \"extrapolando\". La libertad que tiene el polinomio de interpolaci\363n en puntos situados a la derecha e izquierda del sopo rte conduce a que con extrapolaci\363n se obtengan, en general, peores resultados. " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "p(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&-%$expG6# \"\"\"F(%\"xGF($\"+++++?!\"*F%$!+++++5F,F)$!+UDW(H$F,$\"+UDW(H$F,F(" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 " (c) Por \372ltimo, el soporte tiene ahora tres puntos:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 68 "p:=proc(x::uneval) interp([0,1,2], [exp(0), \+ exp(1), exp(2)], x) end;" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pGR6#'%\"xG%'unevalG6\"F*F*-% 'interpG6%7%\"\"!\"\"\"\"\"#7%-%$expG6#F/-F46#F0-F46#F19$F*F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(p(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"$\"+AiCw9!\"*F&$\"*1c.U#F+$\" \"\"\"\"!F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "z:=evalf(p(y ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,(*$)%\"yG\"\"#\"\"\"$\"+ AiCw9!\"*F($\"*1c.U#F-$\"\"\"\"\"!F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "y:=.25;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG$\"#D !\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+!HuF:\"!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "El error cometido en la aproximaci\363n es" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "abs(z-exp(.25));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*F6DJ\"!\"*" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 79 "De nuevo comparamos las gr\341ficas de la funci \363n y su polinomio de interpolaci\363n:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot([p(x),exp(x)],x=-1..1); " }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7S7$$!\"\"\"\"!$\"1;Nb81@ MA!#:7$$!1nmm;p0k&*!#;$\"1]p'\\nb)=@F-7$$!1LL$3F-7$$!1mmm\"4m(G$)F1$\"10C%)ps%HaF1$\"1 %*HrZDx.8F-7$$!1+++]$*4)*\\F1$\"1\")QhC#4yC\"F-7$$!1+++]_&\\c%F1$\"1OR UoS9(>\"F-7$$!1+++]1aZTF1$\"1>kK-+c`6F-7$$!1nm;/#)[oPF1$\"1+%)GB$Q%=6F -7$$!1MLL$=exJ$F1$\"1([&*o_'>#3\"F-7$$!1MLLL2$f$HF1$\"1[kFfy=c5F-7$$!1 ++]PYx\"\\#F1$\"1)4tdV\\8.\"F-7$$!1MLLL7i)4#F1$\"1cg9$*GA95F-7$$!1++]P 'psm\"F1$\"1eM+aEo+5F-7$$!1++]74_c7F1$\"1Wb9lN&*G**F17$$!1JLL$3x%z#)!# <$\"1r@CpM!3!**F17$$!1MLL3s$QM%Fer$\"1INgY)=F#**F17$$!1^omm;zr)*!#>$\" 1[>Eh]i(***F17$$\"1\"F-7$$\"1lmmmZvOL F1$\"1O5f-c7X7F-7$$\"1+++]2goPF1$\"1*ychBv3I\"F-7$$\"1KL$eR<*fTF1$\"1$ QgP$z9c8F-7$$\"1+++])Hxe%F1$\"1T=!\\&)[F-7$$\"1mm;HYt7vF1$\"1-PaRd/:?F-7$$ \"1*******p(G**yF1$\"1&[U>-]B6#F-7$$\"1mmmT6KU$)F1$\"1k?_DuHHAF-7$$\"1 LLLLbdQ()F1$\"1FXZ^h!)QBF-7$$\"1++]i`1h\"*F1$\"1f&F17$F\\o$\"11uvRHL5eF17$Fao$\"1h`=4&fk1'F17$Ffo$\"1o)*)HW )*\\L'F17$F[p$\"1Sdj9q-0mF17$F`p$\"1d1T#y(>goF17$Fep$\"16<*Q)=[wrF17$F jp$\"1!y\\.E)zbuF17$F_q$\"1wFu%Q;Wz(F17$Fdq$\"18-HV,'p5)F17$Fiq$\"1.F] goIk%)F17$F^r$\"1.[k;i@>))F17$Fcr$\"1ad-&\\+a?*F17$Fir$\"1i#G[g:\\d*F1 7$F^s$\"1%)QMzI8!***F17$Fds$\"1Z0q6.0W5F-7$Fis$\"1t^ka\\!\\3\"F-7$F^t$ \"1(zM@lE38\"F-7$Fct$\"1$e]g`5.=\"F-7$Fht$\"1E;`;c\"3B\"F-7$F]u$\"1&y' 4$)zt\"G\"F-7$Fbu$\"1'>'[,1vS8F-7$Fgu$\"1+#pi+!4'R\"F-7$F\\v$\"1IAQE.q d9F-7$Fav$\"1!RtqMte^\"F-7$Ffv$\"1E+V%\\J@e\"F-7$F[w$\"1]tZ?v6Z;F-7$F` w$\"1%f'fjF-7$Fdx$\"1vSfBwPK?F-7$Fix$\"1J]$\\l(p>@F-7$F^y$\"1i!=R[RK?#F-7 $Fcy$\"1=Ad$*[/.BF-7$Fhy$\"1`]xri8'R#F-7$F]z$\"1WqM`&R&*\\#F-7$Fbz$\"1 sQsflo-EF-Ffz-F\\[l6&F^[lF*F_[lF*-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$; F(Fgz%(DEFAULTG" 2 267 267 267 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 279 "Este caso es de interpolaci\363n. Sin embargo, tambi\351n la situ aci\363n empeora con respecto al primer caso. Obs\351rvese que, ahora, los puntos del soporte est\341n m\341s lejos del punto cuya imagen se quiere aproximar que en el primer caso, por lo que no resulta extra \361o este \"empeoramiento\"." }}}}}{MARK "2 32 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 }