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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{EXCHG {PARA 262 "" 0 "" {TEXT 275 1 " " }{TEXT 287 33 "An\341lisis \+
Complejo - Matem\341tica 4 " }}{PARA 257 "" 0 "" {TEXT -1 1 "\n" }
{TEXT 276 15 "TALLER DE MAPLE" }}{PARA 263 "" 0 "" {TEXT -1 0 "" }}
{PARA 260 "" 0 "" {TEXT -1 14 " LABORATORIO 1" }}{PARA 259 "" 0 "" 
{TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 133 "En este laborat
orio vamos a trabajar con sucesiones de n\372meros reales y complejos.
 Tambi\351n se ver\341 c\363mo definir y graficar funciones." }}{PARA 
0 "" 0 "" {TEXT -1 120 " Veamos algunos ejemplos en los que se usan  l
os distintos comandos que necesitar\341. Para ello cliquee en el signo
 (+). \n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Asignaci\363n\n" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 223 "\nUno puede pensar que la memoria
 de una computadora est\341 formada por buzones cada uno de ellos con \+
un nombre  o  direcci\363n. En cada uno de estos buzones o cajitas se \+
puede guardar una informac\363n.\n\nEn la caja  con direcci\363n " }
{TEXT 256 1 "a" }{TEXT -1 14 " (la variable " }{TEXT 257 1 "a" }{TEXT 
-1 54 ") guardamos el n\372mero entero 3 usando el  s\355mbolo de  " }
{TEXT 258 10 "asignaci\363n" }{TEXT -1 4 "   \"" }{TEXT 259 5 " : = " 
}{TEXT -1 83 " \" y seguido de un punto y coma. Para ejecutar este com
ando debe apretar la tecla  " }{TEXT 260 5 "Enter" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 6 "a:=3; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
50 "Maple busca el contenido de la caja con direcci\363n " }{TEXT 261 
1 "a" }{TEXT -1 18 " con el  comando  " }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 2 "a;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Ahora escribimos" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=b;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "b:=c;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "c:=
4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 50 "Contestar (mentalmente) las siguientes preguntas:
\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "1.- \277Cu\341les son los v
alores de " }{TEXT 262 1 "a" }{TEXT -1 2 ", " }{TEXT 263 1 "b" }{TEXT 
-1 3 " y " }{TEXT 264 1 "c" }{TEXT -1 2 " ?" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "2.- Si asigna a " }{TEXT 265 1 
"b" }{TEXT -1 40 " el valor 56, \277qu\351 valores toman a, b y " }
{TEXT 267 1 "c" }{TEXT -1 18 "?                 " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b:=56;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 2 "b;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "c;
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
39 " Uno puede guardar en una variable una " }{TEXT 268 9 "expresi\363
n" }{TEXT 282 1 " " }{TEXT 289 10 "aritm\351tica" }{TEXT -1 14 ",  por
 ejemplo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a:=3*d+e;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "Le
 asignamos a  " }{TEXT 271 1 "d" }{TEXT -1 2 " y" }{TEXT 279 1 " " }
{TEXT 272 1 "e" }{TEXT -1 94 " los valores 3 y 4 respectivamente y lue
go le preguntamos a Maple por el valor de la variable " }{TEXT 273 1 "
a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "d:=3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "e:=
4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 41 "Si uno quiere asignarle a las  variables " }
{TEXT 269 1 "d" }{TEXT -1 3 " y " }{TEXT 270 1 "e" }{TEXT -1 87 " nuev
amente su valor simb\363lico , o sea \"vaciar\" el contenido de las ca
jas, escribimos\n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " e:='e';" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 11 "El comando " }{TEXT 288 5 "evalf" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 11 "El comando " }{HYPERLNK 17 "evalf" 2 "evalf" "" }{TEXT 
-1 114 "  da el valor en aritm\351tica en punto flotante de un n\372me
ro real con la cantidad de d\355gitos que uno quiera indicar." }}}
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalf(sqrt(2),20);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(Pi,190);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{SECT 
1 {PARA 3 "" 0 "" {TEXT -1 10 "Sucesiones" }{MPLTEXT 0 21 0 "" }{TEXT 
-1 1 "\n" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 11 "El comando " }{TEXT 
264 3 "seq" }}{PARA 0 "" 0 "" {TEXT -1 69 "Para generar sucesiones (nu
m\351ricas o no) podemos utilizar el comando " }{HYPERLNK 17 "seq" 2 "
seq" "" }{TEXT 256 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 7 "Ejemplo" }}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 25 "Guardemos en la variable " }{TEXT 286 5 "pares" }{TEXT -1 50 " \+
la sucesi\363n de los primeros veinte n\372meros pares:" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "pares:
=seq (2*i,i=1..10);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 45 "Podemos luego acceder a la sucesi\363n completa
 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "pares;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 32 "o a alg\372n elemento en particular" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 9 "pares[3];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "pares[1]+
pares[10];" }}}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 10 "El comando" }{TEXT 266 1 " " }{TEXT 290 
15 "for ...do... od" }{TEXT 291 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {HYPERLNK 17 "For...do" 2 "for" "" }{TEXT -1 143 "
 se emplea para repetir un cierto n\372mero de veces una serie de inst
rucciones y se puede utilizar para generar sucesiones elemento por ele
mento." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" 
{TEXT 260 9 "Ejemplos\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 41 "Generemos los n\372meros pares del 2 al 2
0:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "for k from 1 to 10 \+
do;\n   2*k;\n od;\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Otra form
a es:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "for k from 2 to \+
20 by 2 do;\nk;\nod;\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Asignem
os un nombre a cada elemento:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 37 "for k from 1 to 10 do;\na[k]:=2*k;\nod;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 6 "a[5];\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 11 "a[1]+a[10];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
}}{SECT 1 {PARA 4 "" 0 "Sucesiones...Plot" {TEXT -1 11 "El comando " }
{TEXT 265 4 "plot" }{TEXT -1 1 "\n" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
1 " " }{HYPERLNK 17 "Plot" 2 "plot" "" }{TEXT -1 39 " se utiliza para \+
graficar funciones  o " }{HYPERLNK 17 " listas" 2 "list" "" }{TEXT -1 
38 " de puntos. Vamos a usar esto \372ltimo.\n" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 258 9 "Ejemplos\n" }
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "plot ([[1.2,
1.8],[2,2],[1,-1]],style=POINT);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 43 "plot ([[1.2,1.8],[2,2],[1,-1]],style=LINE);" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "plot([[1.2,
1.8],[2,2],[1,-1],[1.2,1.8]],style=LINE,color=BLUE);" }{TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 46 "Grafiquemos la sucesi\363n real 1/n en el plano:\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a:=seq([n,1/n],n=1..30);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot([a],style=point);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 39 "Grafiquemos las sucesiones de n\372meros  " }{TEXT 268 
10 "complejos " }{XPPEDIT 18 0 "(1+.5e-1*I)^n;" "6#),&\"\"\"F%*&-%&Flo
atG6$\"\"&!\"#F%%\"IGF%F%%\"nG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "(.9+.
5e-1*I)^n;" "6#),&-%&FloatG6$\"\"*!\"\"\"\"\"*&-F&6$\"\"&!\"#F*%\"IGF*
F*%\"nG" }{TEXT -1 3 " y " }{XPPEDIT 18 0 "((1+.5e-1*I)/sqrt(1.0025))^
n;" "6#)*&,&\"\"\"F&*&-%&FloatG6$\"\"&!\"#F&%\"IGF&F&F&-%%sqrtG6#-F)6$
\"&D+\"!\"%!\"\"%\"nG" }{TEXT -1 74 " que, aunque parecidas, tienen co
mportamientos bien distintos (\277por qu\351?):" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "z1:=(1+0.05
*I);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "a:=seq(z1^n,n=1..20
0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "A:=plot\n([seq([Re(a
[n]),Im(a[n])],n=1..200)],style=POINT,scaling=CONSTRAINED):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "A;\n\n" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "
z2:=(0.99+0.05*I);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "b:=se
q(z2^n,n=1..300):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "B:=p
lot ([seq ([Re(b[n]),Im(b[n])],n=1..300)],style=POINT,color=GREEN,scal
ing=CONSTRAINED):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "B;\n\n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "z3:=(1+0.05*I)/(1.0025)
^(1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "c:=seq(z3^n,n=1.
.200):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "C:=plot ([seq ([R
e(c[n]),Im(c[n])],n=1..200)],style=POINT,color=YELLOW,scaling=CONSTRAI
NED):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "C;\n\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 63 "Si queremos ver los tres gr\341ficos juntos utilizamos el coman
do " }{HYPERLNK 17 "display" 2 "display" "" }{TEXT -1 43 ".  Este coma
ndo se encuentra en el paquete " }{HYPERLNK 17 "plots" 2 "plots" "" }
{TEXT 257 2 " ," }{TEXT -1 50 " el cual antes deber\341 ser \"bajado\"
 con el comando " }{HYPERLNK 17 "with:" 2 "with" "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display([A,B,C],axe
s=FRAMED);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 204 "En estos tres ejemplos se han utilizado \+
como bases n\372meros complejos con argumento peque\361o, \277qu\351 p
asar\355a si no?; \277y si el m\363dulo no es cercano a uno? Pruebe a \+
cambiar las bases en los ejemplos anteriores." }}}}}{SECT 1 {PARA 4 "
" 0 "" {TEXT -1 13 "Animaciones\n\n" }}{EXCHG {PARA 0 "" 0 "Sucesiones
...Animaciones" {TEXT -1 53 "Para animar gr\341ficos se pueden utiliza
r los comandos " }{HYPERLNK 17 "animate" 2 "animate" "" }{TEXT -1 3 " \+
y " }{HYPERLNK 17 "display" 2 "plots,display" "" }{TEXT -1 41 ". Utili
zaremos este \372ltimo con la opci\363n " }{TEXT 261 16 "insequence= t
rue" }{TEXT -1 60 ".\nRecuerde que para usar estos comandos antes debe
 ejecutar " }{HYPERLNK 17 "with(plots)" 2 "plots" "" }{TEXT 259 2 ";\n
" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Ejemplos\n" }}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 35 "Animemos el gr\341fico de la sucesi\363n " }
{XPPEDIT 18 0 "(.8+.5*I)^n;" "6#),&-%&FloatG6$\"\")!\"\"\"\"\"*&-F&6$
\"\"&F)F*%\"IGF*F*%\"nG" }{TEXT -1 2 ".\n" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 11 "z:=.8+.5*I;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "d:=s
eq(plot([[Re(z^n),Im(z^n)]]),n=1..50):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "display ([d],style=POINT,insequence=true,scaling=cons
trained);" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 6 "Nota: " }{TEXT 
-1 173 "para comenzar la animaci\363n haga \"click\" con el bot\363n i
zquierdo del \"mouse\" sobre el gr\341fico y luego sobre el bot\363n \+
\"play\" que aparecer\341 en la parte superior de la pantalla.\n" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 263 16 "Insequence=false" }{TEXT -1 37 " \+
muestra todos los \"cuadros\" juntos:\n" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "display ([d
],style=POINT,insequence=false,scaling=constrained);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 98 " Para visualiza
r la sucesi\363n del ejemplo anterior como vectores en el origen supri
mimos la opci\363n " }{TEXT 256 11 "style=POINT" }{TEXT -1 2 ": " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 60 "d:=seq(plot([[0,0],[Re(z^n),Im(z^n)]],color=BLACK),n=1..50):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "display ([d],insequence=tru
e,axes=BOXED,scaling=constrained);" }}{PARA 13 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "display([d],insequence=fal
se,axes=BOXED,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Si desea graf
icar los vectores como flechas puede usar el comando " }{HYPERLNK 17 "
arrow" 2 "arrow" "" }{TEXT -1 14 "  en lugar de " }{TEXT 267 4 "plot" 
}{TEXT -1 2 ".\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "
Funciones\n" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 36 "Definiciones de fu
nci\363n y expresi\363n\n" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Defin
imos la  funci\363n  " }{XPPEDIT 18 0 "f(x) = x^3+3;" "6#/-%\"fG6#%\"x
G,&*$F'\"\"$\"\"\"F*F+" }{TEXT -1 1 "," }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "f:=x->x^3+3;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 28 "\277Funciona como una funci\363n?\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "f(u);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 98 "Vemos que funciona precisam
ente como se espera que una funci\363n lo haga. Observe que, para MAPL
E,  " }{TEXT 256 1 "f" }{TEXT -1 12 "  no es una " }{TEXT 257 9 "expre
si\363n" }{TEXT -1 10 " sino una " }{TEXT 258 7 "funci\363n" }{TEXT 
-1 12 ". En cambio " }{TEXT 261 5 "f(x) " }{TEXT -1 7 "es una " }
{TEXT 262 9 "expresi\363n" }{TEXT -1 10 " y no una " }{TEXT 263 9 "fun
ci\363n. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "\nUna " }{TEXT 259 9 
"expresi\363n" }{TEXT -1 31 " puede ser transformada en una " }{TEXT 
260 7 "funci\363n" }{TEXT -1 17 "  con el comando " }{HYPERLNK 17 "una
pply" 2 "unapply" "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "g:=sqrt(3*x-
6);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "g:=unapply(g,x);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(6);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Defina
mos la funci\363n " }{XPPEDIT 18 0 "h(x) = x^2-y^2;" "6#/-%\"hG6#%\"xG
,&*$F'\"\"#\"\"\"*$%\"yGF*!\"\"" }{TEXT -1 1 "," }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "h:=(x,y)->x^2-y^2;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 7 "h(1,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "
" 0 "" {TEXT 283 11 "El comando " }{TEXT 256 4 "plot" }{TEXT -1 1 "\n
" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Para graficar " }{TEXT 257 25 
"funciones de una variable" }{TEXT -1 25 " utilizaremos el comando " }
{HYPERLNK 17 "plot" 2 "plot" "" }{TEXT -1 2 ".\n" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 15 "f:=x->tan(3*x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "plot(f(x),x=-4..4);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "y si consider
amos necesario para ver mejor la figura, acotamos el eje de las " }
{TEXT 256 3 "y,\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(f
(x),x=-4..4,-5..5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "\nOtro ejemplo:" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "y:= 15*si
n(x)/x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot(y,x=-20..20
,color=pink);  " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Observe que he
mos podido elegir el color con el que quer\355amos dibujar. " }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "Tambi\351n pode
mos dibujar dos gr\341ficos juntos" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "plot(\{x^2/10,y\},x=-10..10);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 261 "" 0 "" {TEXT -1 10 "El
 comando" }{TEXT 284 1 " " }{TEXT 256 6 "plot3d" }{TEXT -1 0 "" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Para graficar " }{TEXT 256 25 "fun
ciones de dos variable" }{TEXT -1 26 "s utilizaremos el comando " }
{HYPERLNK 17 "plot3d" 2 "plot3d" "" }{TEXT -1 2 ".\n" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 31 "Primero \"limpiemos\" la memoria," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "z:=x^2-y^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 57 "plot3d(z,x=-4..4,y=-4..4,axes=boxed,orientation=[76,46]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 33 "Grafiquemos dos funciones juntas;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "f:=ln(x^2*y^4+exp(2))+7;" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 5 "g:=9;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 30 "plot3d(\{f,g\},x=-2..2,y=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{PARA 5 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 
3 "" 0 "" {TEXT -1 23 "Sucesiones de funciones" }}{PARA 0 "" 0 "" 
{TEXT -1 53 "Para animar gr\341ficos se pueden utilizar los comandos \+
" }{HYPERLNK 17 "animate" 2 "animate" "" }{TEXT -1 3 " y " }{HYPERLNK 
17 "display" 2 "plots,display" "" }{TEXT -1 60 ". Recuerde que para us
ar estos comandos antes debe ejecutar " }{HYPERLNK 17 "with(plots)" 2 
"plots" "" }{TEXT -1 21 ". Tambi\351n puede ver  " }{HYPERLNK 17 "Suce
siones...Animaciones" 1 "" "Sucesiones...Animaciones" }{TEXT -1 2 ".\n
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "with(plots,display);" }}}{PARA 5 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "Veamos c\363mo converge la suce
si\363n de funciones definida por    " }{XPPEDIT 18 0 "f[n];" "6#&%\"f
G6#%\"nG" }{TEXT -1 0 "" }{TEXT 258 4 "(x)=" }{XPPEDIT 18 0 "n/(n+4)*s
in(x);" "6#*(%\"nG\"\"\",&F$F%\"\"%F%!\"\"-%$sinG6#%\"xGF%" }{TEXT -1 
19 "    a la funci\363n   " }{XPPEDIT 18 0 "f(x) = sin(x);" "6#/-%\"fG
6#%\"xG-%$sinG6#F'" }{TEXT -1 31 ". \277La convergencia es uniforme?" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 55 "fn:=seq( plot ( n/(n+4)*sin(x),x=-2*Pi..2*Pi),n=1..30):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "display ([fn],insequence=tru
e);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 5 "NOTA:" }
{TEXT -1 110 " para comenzar la animaci\363n presione el bot\363n izqu
ierdo del \"mouse\" sobre el gr\341fico y luego el bot\363n \"play\".
\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "display ([fn],inseque
nce=false);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "fn:=seq( plo
t ( [sin(x),n/(n+4)*sin(x)],x=-2*Pi..2*Pi),n=1..40):" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 31 "display ([fn],insequence=true);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 132 "Observe que la convergencia parece ir disminuyendo su velocida
d, por qu\351? Adem\341s los gr\341ficos est\341n cada vez m\341s cerc
a uno de otro (" }{XPPEDIT 18 0 "f[n];" "6#&%\"fG6#%\"nG" }{TEXT -1 
13 " converge => " }{XPPEDIT 18 0 "f[n];" "6#&%\"fG6#%\"nG" }{TEXT -1 
17 " es de Cauchy).\n\n" }}}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{SECT 1 
{PARA 5 "" 0 "" {TEXT 285 31 "Funciones de variable compleja\n" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
32 "restart:\nwith(plots,conformal):\n" }}}{EXCHG {PARA 0 "" 0 "...de \+
variable compleja" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "La ins
trucci\363n " }{TEXT 256 0 "" }{HYPERLNK 17 "conformal" 2 "conformal" 
"" }{TEXT -1 255 " permite interpretar gr\341ficamente funciones de va
riable compleja a valores complejos mostrando la imagen de la funci
\363n aplicada a una cuadr\355cula (o grilla). Esta se determina indic
ando dos v\351rtices de una de las diagonales y la cantidad de subdivi
siones.\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "La grilla con v\351r
tices 0+0*I, 1+2*I con 8 divisiones horizontales y 10 verticales es:\n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "conformal (z, z=0..1+2*
I,grid=[10,8],scaling=constrained,axes=framed);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 59 "Veamos c\363mo transforma esta grilla la funci\363n \+
exponencial  " }{XPPEDIT 18 0 "exp(x+I*y) = exp(x)*(cos(y)+I*sin(y));
" "6#/-%$expG6#,&%\"xG\"\"\"*&%\"IGF)%\"yGF)F)*&-F%6#F(F),&-%$cosG6#F,
F)*&F+F)-%$sinG6#F,F)F)F)" }{TEXT -1 2 ":\n" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 62 "conformal (exp(z),z=0..1+2*I,grid=[10,8],scaling=c
onstrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 432 "Observe c\363mo \+
la funci\363n exponencial transforma cada segmento horizontal (en verd
e) d\341ndole una inclinaci\363n  constante igual a la parte imaginari
a mientras que los verticales (en rojo) se curvan pues sobre ellos la \+
parte imaginaria crece. Adem\341s los segmentos verticales se transfor
man en arcos de circunferencias (\277por qu\351?) Otra observaci\363n \+
es que los \341ngulos donde se cortan las im\341genes de los segmentos
 son  rectos (\277por qu\351?).\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
122 "En el ejemplo siguiente veremos (con animaci\363n) c\363mo se com
porta la exponencial a medida que aumenta la parte imginaria. \n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart:\nwith (plots):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "G:=seq(conformal(z,z=0..1+I*t/8,gr
id=[5,10],scaling=constrained),t=1..60):\nF:=seq(conformal(exp(z),z=0.
.1+I*t/8,grid=[5,10],scaling=constrained),t=1..60):" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 101 "display ([G],insequence=true,scaling=constrained)
;\ndisplay ([F],insequence=true,scaling=constrained);" }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 117 "En el ejempl
o siguiente veremos (con animaci\363n) c\363mo se comporta la exponenc
ial a medida que aumenta la parte real. \n" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 22 "restart:\nwith (plots):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 152 "G:=seq(conformal(z,z=0..t/10+I,grid=[15,5],scaling=c
onstrained),t=1..20):\nF:=seq(conformal(exp(z),z=0..t/10+I,grid=[15,5]
,scaling=constrained),t=1..20):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "display ([G],insequence=true,s
caling=constrained);\ndisplay ([F],insequence=true,scaling=constrained
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{SECT 0 {PARA 4 "" 0 "" {TEXT 274 12 "Ejercitaci\363n" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Abrir una nue
va hoja de trabajo (worksheet) cliqueando debajo del men\372 " }{TEXT 
256 4 "File" }{TEXT -1 11 " la opci\363n " }{TEXT 257 3 "New" }{TEXT 
-1 101 " y realizar los siguientes ejercicios. Para guardar el conteni
do de la misma, elegir debajo del men\372 " }{TEXT 260 4 "File" }
{TEXT -1 16 " la alternativa " }{TEXT 261 7 "Save as" }{TEXT -1 74 ". \+
 A medida que avance el laboratorio se recomienda elegir la alternativ
a " }{TEXT 262 4 "Save" }{TEXT -1 41 " a fin de guardar lo que ya est
\341  hecho. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT 277 1 "1" }{TEXT -1 108 ".- Ejecutar los siguientes comandos \+
y anotar las respuestas que devuelve Maple. \n(a) Guardar en la variab
le " }{TEXT 263 2 " g" }{TEXT -1 4 "  la" }{TEXT 265 1 " " }{TEXT 293 
9 "expresi\363n" }{TEXT 292 1 " " }{TEXT -1 1 " " }{XPPEDIT 18 0 "sqrt
(x^2+4);" "6#-%%sqrtG6#,&*$%\"xG\"\"#\"\"\"\"\"%F*" }{TEXT -1 1 "." }}
{PARA 0 "" 0 "" {TEXT -1 26 "(b) Guardar en la variable" }{TEXT 264 1 
" " }{TEXT 294 1 "f" }{TEXT 295 1 " " }{TEXT -1 4 "la  " }{TEXT 280 7 
"funci\363n" }{TEXT 266 1 " " }{TEXT -1 1 " " }{XPPEDIT 18 0 "f(x) = x
^2+sin(x);" "6#/-%\"fG6#%\"xG,&*$F'\"\"#\"\"\"-%$sinG6#F'F+" }{TEXT 
-1 34 "\n(c) \277Cu\341l es el valor de f(2), f(" }{TEXT 267 2 "t)" }
{TEXT -1 4 ", f(" }{TEXT 268 1 "a" }{TEXT -1 10 "+2)  y  f(" }
{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 3 ") ?" }}{PARA 0 "" 0 "" 
{TEXT -1 36 "(d) Calcular un valor num\351rico de f(" }{XPPEDIT 18 0 "
Pi;" "6#%#PiG" }{TEXT -1 18 ") con 150 d\355gitos." }}{PARA 0 "" 0 "" 
{TEXT -1 19 "(e) Transformar la " }{TEXT 278 10 " expresi\363n" }
{TEXT -1 14 "  guardada en " }{TEXT 269 1 " " }{TEXT 296 1 "g" }{TEXT 
-1 33 " en una  funci\363n  con el comando " }{TEXT 275 7 "unapply" }
{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 281 1 "2" }{TEXT -1 2 ".-" }}
{PARA 0 "" 0 "" {TEXT -1 34 "(a) Resolver (a mano) la ecuaci\363n " }
{XPPEDIT 18 0 "sqrt(-x^2+1) = -x;" "6#/-%%sqrtG6#,&*$%\"xG\"\"#!\"\"\"
\"\"F,,$F)F+" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 28 "(b) Grafi
car las funciones  " }{XPPEDIT 18 0 "f(x) = sqrt(-x^2+1);" "6#/-%\"fG6
#%\"xG-%%sqrtG6#,&*$F'\"\"#!\"\"\"\"\"F/" }{TEXT -1 6 "  y   " }
{XPPEDIT 18 0 "h(x) = -x;" "6#/-%\"hG6#%\"xG,$F'!\"\"" }{TEXT -1 120 "
   en un mismo  gr\341fico.    \n(c) Comparar las respuestas obtenidas
 en los puntos (a) y (b).                             " }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 
3 "" 0 "" {TEXT -1 45 "Proyeci\363n estereogr\341fica: galer\355a de d
ibujos." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 53 "Veamos algunos dibujos realizados con MAPLE sobre la " }
{TEXT 256 25 "proyecci\363n estereogr\341fica" }{TEXT -1 1 "." }}
{PARA 0 "" 0 "" {TEXT -1 81 "Estos fueron realizados con el programa q
ue se encuentra al final de la secci\363n.\n" }}}{EXCHG {PARA 259 "" 
0 "" {TEXT -1 72 "La proyecci\363n de una circunferencia es una circun
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{TEXT 258 11 "Ant\355podas: " }{TEXT 259 0 "" }{TEXT -1 126 "la curva \+
negra es la imagen de la roja despu\351s de haberle aplicado la transf
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. Las proyecciones de estas curvas son " }{TEXT 260 10 "ant\355podas \+
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plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "##Entre en c1(t) la curva en el plano con a<t<b." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "##esfera de radio 1:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "S:=sphereplot(1
,theta=0..2*Pi,phi=0..Pi,style=patchnogrid,scaling=constrained):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "## Polo Norte" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "n:=[0,0,1]:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "N:=pointplot3d(
\{n\},color=red):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
35 "###################################" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "c1:=t->(cos(t)+3,sin(t),
0): ########-----> Cambie por la curva que quiera " }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 5 "a:=0:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "b:=2*Pi:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "###############
####################" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "##Plano z=0" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "P:=plot3
d([x,y,0],x=-2..4.1,y=-2..2,scaling=constrained,style=PATCHNOGRID,colo
r=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 45 "## T es la Proyeccion Estereografica de P ->S
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 70 "T:=(x,y,z)->(2*x/(x^2+y^2+1),2*y/(x^2+y^2+1),(x^2+y^2
-1)/(x^2+y^2+1)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "## Regio
n en P:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "C1:=spacecurve([c1(t),t=a..b],color=RED):" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "## Region en S:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 45 "Tc1:=spacecurve([T(c1(t)),t=a..b],color=RED)
:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "##Rectas de la proyeccion" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "r:=t->spacecurv
e(convert(evalm([c1(t)]*(1-s)+n*s),list),s=0..1,color=yellow):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
37 "rectas:=seq(r(a+(b-a)*u/20),u=0..20):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "##Dibuja
r:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 114 "display(\{C1,Tc1,P,S,N,rectas\},axes=boxed,scaling=c
onstrained,\norientation=[42,73],view=[-1.2..4,-1.2..1.2,-1..1]);" }}}
}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{MARK "2 0 0" 0 }{VIEWOPTS 1 1 0 1 
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }