{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 0 0 0 0 0 0 2 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 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{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 "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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 11 "%%%%%%%%%% " }{TEXT 256 45 "C\301LCULO SIMB\323LIC O FRENTE AL C\301LCULO NUM\311RICO:" }{TEXT -1 21 " %%%%%%%%%%%%%%%%%% %%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 109 " - La principal diferencia entre Maple y una calc uladora de mano es que para Maple los n\372meros \"son exactos\":" }} {PARA 0 "" 0 "" {TEXT -1 211 "Si en una calculadora escribimos 1/3, el resultado ser\341 del tipo 0,33333333333333333333333333333333, donde \+ el n\372mero de decimales depender\341 de la precisi\363n de la m\341q uina. Sin embargo, en Maple el resultado es..." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "1/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\" \"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 118 " Si queremos que Maple \+ haga el c\341lculo de manera num\351rica, tenemos dos opciones; una es aproximar el valor anterior..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf(1/3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+LLLLL!#5" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 99 " El n\372mero de decimales que m aneja Maple est\341 almacenado en el valor \"Digits\", que podemos cam biar:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Digits;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Digits:=20; evalf(1/3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%' DigitsG\"#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"5LLLLLLLLLL!#?" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=10:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 117 " La otra es decirle que \"1\" es un valo r num\351rico, escribi\351ndolo como 1.0 (en forma abreviada 1. con un punto detr\341s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "1./3; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+LLLLL!#5" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 129 " %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%\n \277De verdad hay tanta diferencia? \277Por qu\351 es esto importante?" }}{PARA 0 "" 0 "" {TEXT -1 65 "%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 " Si s umamos simb\363licamente 1/3+1/3, el resultado es..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "1/3+1/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6##\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 115 " Sumando num \351ricamente; si 1/3 es 0.3333333333, la suma de 1/3+1/3 deber\355a s er 0.3333333333+0.3333333333, que es..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "1./3+1./3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+mmm mm!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 " Sin embargo, una calcu ladora de mano \"hace trampas\" y no da ese resultado, sino 0.66666666 67 \277por qu\351?" }}{PARA 0 "" 0 "" {TEXT -1 122 "Esta cantidad es l a misma que nos da si le pedimos que calcule 2/3; en realidad, no est \341 sumando 0.3333333333+0.3333333333" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "2./3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+nmmmm!#5 " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 140 " Vale, entonces en este ejem plo nuestra calculadora de mano es capaz de hacer trampas cuando le in teresa para darnos el resultado verdadero." }}{PARA 0 "" 0 "" {TEXT -1 61 "Pero \277es capaz de hacer lo mismo en ejemplos m\341s complica dos?" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A1:=(2^Pi)^(Pi+7893/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G))\"\"#%#PiG,&F(\"\"\"#\"%$*yF'F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "A2:=(sqrt(2^Pi))^(2*Pi+7893);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G)*$-%%sqrtG6#)\"\"#%#PiG\"\"\",& F,F+\"%$*yF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "A:=A1/A2;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG*&))\"\"#%#PiG,&F)\"\"\"#\"%$*y F(F+F+)*$-%%sqrtG6#F'F+,&F)F(F-F+!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+17++5 !\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(A);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 181 " Incluso, si el ejemplo es demasiado complicado, quiz \341 esa divisi\363n no sea posible de realizar num\351ricamente si no nos damos cuenta de que el numerador y el denominador son iguales:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "B1:=sqrt(((sqrt(2)+sqrt(3) )^3+2^(Pi)))^(2*Pi^19);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B1G)*$-% %sqrtG6#,&*$),&*$-F(6#\"\"#\"\"\"F2*$-F(6#\"\"$F2F2F6F2F2)F1%#PiGF2F2, $*$)F8\"#>F2F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "B2:=expan d(B1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B2G),(*$-%%sqrtG6#\"\"#\" \"\"\"#6*&\"\"*F,-F)6#\"\"$F,F,)F+%#PiGF,*$)F4\"#>F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "B:=B2/B1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG*&),(*$-%%sqrtG6#\"\"#\"\"\"\"#6*&\"\"*F--F*6#\"\"$F-F-)F,%#P iGF-*$)F5\"#>F-F-)*$-F*6#,&*$),&F(F-*$F1F-F-F3F-F-F4F-F-,$F6F,!\"\"" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"\"%*undefinedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 200 " %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%\n Buscar otros ejemplos en los que las calculadoras \+ hacen trampas. A veces, \351stas no nos resultan f\341ciles de encontr ar a simple vista:" }}{PARA 0 "" 0 "" {TEXT -1 65 "%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 51 "A1:=sqrt(((sqrt(2)+sqrt(3))^3+2^(Pi)))^(2*Pi+7 893);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G)*$-%%sqrtG6#,&*$),&*$- F(6#\"\"#\"\"\"F2*$-F(6#\"\"$F2F2F6F2F2)F1%#PiGF2F2,&F8F1\"%$*yF2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "A2:=expand(A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G),(*$-%%sqrtG6#\"\"#\"\"\"\"#6*&\"\"*F,-F )6#\"\"$F,F,)F+%#PiGF,,&F4F,#\"%$*yF+F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "A:=A2/A1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG*&) ,(*$-%%sqrtG6#\"\"#\"\"\"\"#6*&\"\"*F--F*6#\"\"$F-F-)F,%#PiGF-,&F5F-# \"%$*yF,F-F-)*$-F*6#,&*$),&F(F-*$F1F-F-F3F-F-F4F-F-,&F5F,F8F-!\"\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(A);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+*R,++\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "tan(arctan(0.2));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+********>!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "tan(arctan(1/5));" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "tan(arctan(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% \"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "28 0 0 " 23 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }