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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" 
{TEXT 273 1 " " }{TEXT 278 43 "An\341lisis I - Matem\341tica 1 - An
\341lisis II (C)" }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "
" {TEXT 274 16 "TALLER DE MAPLE " }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 14 " LABORATORIO 1" }}
{PARA 256 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
328 "En este laboratorio vamos a familiarizarnos con los comandos que \+
MAPLE posee para definir y graficar funciones de una variable real, ha
llar l\355mites, derivar y resolver ecuaciones. Veamos algunos ejemplo
s en los que se usan  los distintos comandos que necesitar\341 para re
solver la ejercitaci\363n. Para ello cliquee en el signo (+). " }}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Asignaci\363n" }}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 223 "\nUno puede pensar que la memoria de una computad
ora est\341 formada por buzones cada uno de ellos con un nombre  o  di
recci\363n. En cada uno de estos buzones o cajitas se puede guardar un
a 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 ") guardamo
s el n\372mero entero 3 usando el  s\355mbolo de  " }{TEXT 258 10 "asi
gnaci\363n" }{TEXT -1 92 "   \" : =  \" y seguido de un punto y coma. \+
Para ejecutar este comando debe apretar la tecla  " }{TEXT 259 5 "Ente
r" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a:=3; " }{TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "MAPLE busca el contenido de la \+
caja con direcci\363n " }{TEXT 260 1 "a" }{TEXT -1 18 " con el  comand
o  " }}{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 10 "Contestar " }
{TEXT 291 13 "(mentalmente)" }{TEXT -1 27 " 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 2 " y" }{TEXT 264 2 " c" }{TEXT -1 2 " ?" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "2.- Si asigna a " }{TEXT 272 1 
"b" }{TEXT -1 33 " el valor 56, \277qu\351 valores toman " }{TEXT 261 
1 "a" }{TEXT -1 2 ", " }{TEXT 273 1 "b" }{TEXT -1 3 " y " }{TEXT 265 
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 3 "c;\n" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 " Uno puede guardar en una variable
 una " }{TEXT 296 10 "expresi\363n " }{TEXT -1 25 "aritm\351tica,  por
 ejemplo\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a:=3*d+e;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "Le
 asignamos a " }{TEXT 269 1 "d" }{TEXT -1 2 " y" }{TEXT 271 2 " e" }
{TEXT -1 13 " los valores " }{XPPEDIT 18 0 "sqrt(2);" "6#-%%sqrtG6#\"
\"#" }{TEXT -1 6 "  y  4" }{XPPEDIT 18 0 "sqrt(2);" "6#-%%sqrtG6#\"\"#
" }{TEXT -1 64 " respectivamente y luego le preguntamos a MAPLE por el
 valor de " }{TEXT 270 1 "a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "d:=sqrt(2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "e:=4*sqrt(2);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 2 "a;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Si \+
uno quiere asignarle a las  variables " }{TEXT 286 1 "d" }{TEXT -1 91 
" y e nuevamente su valor simb\363lico , o sea \"vaciar\" el contenido
 de las cajas, escribimos\n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " e:=
'e';" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "d:='d';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "
" 0 "" {TEXT -1 11 "El comando " }{TEXT 256 5 "evalf" }}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 11 "El comando " }{HYPERLNK 17 "evalf" 2 "evalf" "
" }{TEXT -1 154 "  da el valor en arim\351tica en punto flotante de un
 n\372mero real con la cantidad de d\355gitos que uno indique  (si no \+
se indica nada se mostraran 10 d\355gitos)." }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 11 "evalf(4/3);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "evalf(sqrt(2));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "evalf(Pi,190);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "Funciones y expresio
nes" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 14 "Definimos la  " }{TEXT 293 8 "funci\363n:
" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f:=x->x
^3+3;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "\277Funciona como una fu
nci\363n?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(u);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 72 "Vemos que funciona precisamente como se espera que u
na funci\363n lo haga.\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Consi
deremos ahora la " }{TEXT 292 10 "expresi\363n:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "g:=sqrt(3*x-6);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 4 "Una " }{TEXT 256 9 "expresi\363n" }{TEXT -1 31 " puede ser
 transformada en una " }{TEXT 257 7 "funci\363n" }{TEXT -1 16 " con el
 comando " }{HYPERLNK 17 "unapply" 2 "unapply" "" }{TEXT -1 1 "." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "h:=unapply(g,x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h(6);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 151 "Si en cambio queremos obtener una expresi\363n a partir \+
de una funci\363n, basta con evaluar la funci\363n en una variable cua
lquiera. Por ejemplo, a partir de " }{TEXT 294 1 "f" }{TEXT -1 24 " ob
tenemos la expresi\363n " }{TEXT 295 4 "f(x)" }{TEXT -1 2 ": " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 13 "El  \+
comando  " }{TEXT 256 5 "limit" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 " El comando  " }
{HYPERLNK 17 "limit" 2 "limit" "" }{TEXT -1 27 "  calcula el l\355mite
 de una " }{TEXT 297 9 "expresi\363n" }{TEXT -1 28 ". \nAsignamos a  l
a variable " }{TEXT 298 1 "Q" }{TEXT -1 5 "  la " }{TEXT 258 9 "expres
i\363n" }{TEXT -1 4 "    " }{XPPEDIT 18 0 "(x-1)/(3*x+2);" "6#*&,&%\"x
G\"\"\"F&!\"\"F&,&*&\"\"$F&F%F&F&\"\"#F&F'" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Q:=(x-1)/(3*x+2);" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 
"y calculamos el l\355mite:" }{XPPEDIT 18 0 "limit(Q,x = infinity);" "
6#-%&limitG6$%\"QG/%\"xG%)infinityG" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "limit(Q,x=infinity);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "As
ignamos a  f  la  " }{TEXT 259 7 "funci\363n" }{TEXT -1 3 "   " }
{XPPEDIT 18 0 "proc (x) options operator, arrow; sin(x)/x end;" "6#f*6
#%\"xG7\"6$%)operatorG%&arrowG6\"*&-%$sinG6#F%\"\"\"F%!\"\"F*F*F*" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 15 "f:=x->sin(x)/x;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 13 "y calculamos " }{XPPEDIT 18 0 "limit(f(x)
,x = 0);" "6#-%&limitG6$-%\"fG6#%\"xG/F)\"\"!" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "limit(f(x),
x=0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "\nObserve que el argumen
to del comando " }{TEXT 260 5 "limit" }{TEXT -1 18 "  es la expresi
\363n " }{TEXT 299 4 "f(x)" }{TEXT -1 17 " y no la funci\363n " }
{TEXT 300 1 "f" }{TEXT -1 2 ". " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
70 "\nPodemos tambi\351n calcular el l\355mite por la izquierda o por \+
la derecha:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 20 "limit(Q,x=-2,right);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 14 "Los comando
s  " }{TEXT 256 6 "diff  " }{TEXT 316 1 "y" }{TEXT 317 10 "  simplify
" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
11 "El comando " }{HYPERLNK 17 "diff" 2 "diff" "" }{TEXT -1 12 " deriv
a una " }{TEXT 257 10 "expresi\363n." }{TEXT -1 19 " .  Derivamos las \+
 " }{TEXT 258 10 "expresione" }{TEXT -1 4 "s   " }{TEXT 301 4 "f(x)" }
{TEXT -1 4 "  y " }{TEXT 259 2 " Q" }{TEXT 302 19 ", del \355tem anter
ior" }{TEXT -1 33 " y las guardamos en las variables" }{TEXT 260 4 " d
f " }{TEXT -1 2 "y " }{TEXT 303 3 "dQ " }{TEXT -1 16 "respectivamente.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "df:=diff(f(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "dQ:=diff(Q,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 50 "Simplificamos la ultima expresi\363n
 con el comando  " }{HYPERLNK 17 "simplify" 2 "simplify" "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "dQ:=simplify(dQ);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 14 "Los comandos  " }{TEXT 259 
5 "solve" }{TEXT 318 3 " y " }{TEXT 319 6 "fsolve" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
14 "Los comandos  " }{HYPERLNK 17 "solve" 2 "solve" "" }{TEXT -1 5 "  \+
y  " }{HYPERLNK 17 "fsolve" 2 "fsolve" "" }{TEXT -1 37 "  se usan para
 resolver ecuaciones. \n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Mient
ras que el comando " }{TEXT 256 5 "solve" }{TEXT -1 19 " resuelve en f
orma " }{TEXT 257 6 "exacta" }{TEXT -1 53 " una ecuaci\363n o un siste
ma de ecuaciones, el comando " }{TEXT 258 6 "fsolve" }{TEXT -1 99 " lo
 hace en forma num\351rica. En este caso es conveniente indicar el ran
go donde buscar la soluci\363n. " }}{PARA 0 "" 0 "" {TEXT -1 12 "Por e
jemplo:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "solve(cos(x)=1/3,x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "fsolve(cos(x)=1/3,x=0..Pi/2);" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "fsolve(cos(
x)=1/3,x=11*Pi/2..6*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "p:=t^4+2*t^3-t-2;" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(p=0,t
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "fsolve(p=0,t);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 289 5 "Solve" }{TEXT -1 42 " permite reso
lver inecuaciones sencillas.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 19 "inec:=abs(x-1)<x+2;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 14 "solve(inec,x);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "El \+
comando " }{TEXT 256 4 "plot" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Pa
ra graficar utilizamos el comando " }{HYPERLNK 17 "plot" 2 "plot" "" }
{TEXT -1 1 "." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "En el ejemplo qu
e sigue graficaremos la " }{TEXT 256 10 "expresi\363n " }{TEXT -1 31 "
que guardaremos en la variable " }{TEXT 257 1 "y" }{TEXT -1 1 ":" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "y:= 15*sin(x)/x;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot(y,x=-20..20,color=blue);  " }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Otro ejemplo:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 15 "f:=x->tan(3*x);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 38 "plot(f(x),x=-4..4,-5..5,discont=true);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 77 "N\363tese en el \372ltimo ejemplo que en \+
el comando plot el primer argumento es la " }{TEXT 257 9 "expresi\363n
" }{TEXT -1 1 " " }{TEXT 256 4 "f(x)" }{TEXT -1 1 "." }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 43 "Tambi\351n podemos dibujar dos gr\341ficos junt
os" }}}{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 0 
{PARA 4 "" 0 "" {TEXT 287 12 "Ejercitaci\363n" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Abrir una nueva ho
ja 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 contenido \+
de la misma, elegir debajo del men\372 " }{TEXT 259 4 "File" }{TEXT 
-1 16 " la alternativa " }{TEXT 260 7 "Save as" }{TEXT -1 74 ".  A med
ida que avance el laboratorio se recomienda elegir la alternativa " }
{TEXT 320 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 275 1 "1" }{TEXT -1 80 ".- Realizar las siguientes operaciones c
on  MAPLE. \n(a) Guardar en la variable  " }{TEXT 279 1 "g" }{TEXT -1 
17 "  la  expresi\363n  " }{XPPEDIT 18 0 "sqrt(x^2+4);" "6#-%%sqrtG6#,
&*$%\"xG\"\"#\"\"\"\"\"%F*" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 
-1 27 "(b) Guardar en la variable " }{TEXT 280 2 "f " }{TEXT -1 5 " la
  " }{TEXT 277 8 "funci\363n " }{TEXT -1 1 " " }{XPPEDIT 18 0 "proc (x
) options operator, arrow; x^2+sin(x) end;" "6#f*6#%\"xG7\"6$%)operato
rG%&arrowG6\",&*$F%\"\"#\"\"\"-%$sinG6#F%F.F*F*F*" }{TEXT -1 26 "\n(c)
 \277Cu\341l es el valor de " }{TEXT 304 4 "f(2)" }{TEXT -1 2 ", " }
{TEXT 305 4 "f(t)" }{TEXT -1 2 ", " }{TEXT 306 6 "f(a+2)" }{TEXT -1 5 
"  y  " }{TEXT 307 2 "f(" }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT 309 1 
")" }{TEXT -1 2 " ?" }}{PARA 0 "" 0 "" {TEXT -1 34 "(d) Calcular un va
lor num\351rico de " }{TEXT 308 2 "f(" }{XPPEDIT 18 0 "Pi;" "6#%#PiG" 
}{TEXT 311 1 ")" }{TEXT -1 17 " con 150 d\355gitos." }}{PARA 0 "" 0 "
" {TEXT -1 19 "(e) Transformar la " }{TEXT 276 10 " expresi\363n" }
{TEXT -1 15 "  guardada en  " }{TEXT 290 1 "g" }{TEXT -1 33 " en una  \+
funci\363n  con el comando " }{TEXT 273 7 "unapply" }{TEXT -1 1 "." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 1 "2" }
{TEXT -1 2 ".-" }}{PARA 0 "" 0 "" {TEXT -1 34 "(a) Resolver (a mano) l
a ecuaci\363n " }{XPPEDIT 18 0 "sqrt(1-x^2) = -x;" "6#/-%%sqrtG6#,&\"
\"\"F(*$%\"xG\"\"#!\"\",$F*F," }{TEXT -1 52 ".\n(b) Resolver  la ecuac
i\363n anterior con el comando " }{TEXT 288 5 "solve" }{TEXT -1 1 "." 
}}{PARA 0 "" 0 "" {TEXT -1 27 "(c) Graficar las funciones " }{XPPEDIT 
18 0 "f(x) = sqrt(1-x^2);" "6#/-%\"fG6#%\"xG-%%sqrtG6#,&\"\"\"F,*$F'\"
\"#!\"\"" }{TEXT -1 5 "  y  " }{XPPEDIT 18 0 "h(x) = -x;" "6#/-%\"hG6#
%\"xG,$F'!\"\"" }{TEXT -1 118 " en un mismo gr\341fico.    \n(d) Compa
rar las respuestas obtenidas en los puntos anteriores.                \+
             " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 281 1 "3" }{TEXT -1 25 ".-  Considere la funci\363n " }{XPPEDIT 
18 0 "f(x) = arctan(x/(x-1));" "6#/-%\"fG6#%\"xG-%'arctanG6#*&F'\"\"\"
,&F'F,F,!\"\"F." }{TEXT -1 194 ".\n(a) \277Cu\341l es el dominio de la
 funci\363n?\n........................................................
......................................................................
.................\n\n(b) \277Es " }{TEXT 268 1 "f" }{TEXT -1 25 " una \+
funci\363n continua en " }{TEXT 256 4 "x = " }{TEXT -1 14 "1?  \277Exi
ste el" }{XPPEDIT 18 0 "limit(f(x),x = 1);" "6#-%&limitG6$-%\"fG6#%\"x
G/F)\"\"\"" }{TEXT -1 3 "?  " }}{PARA 0 "" 0 "" {TEXT 257 5 "Ayuda" }
{TEXT -1 54 ": calcule el l\355mite por la izquierda y por la derecha \+
" }}{PARA 0 "" 0 "" {TEXT -1 144 "....................................
......................................................................
......................................" }}{PARA 0 "" 0 "" {TEXT -1 
218 "\n(c) \277Tiene la funci\363n as\355ntotas horizontales? En caso \+
afirmativo \277Cu\341les?\n...........................................
......................................................................
.............................." }}{PARA 0 "" 0 "" {TEXT -1 62 "\n(d) H
allar los intervalos de crecimiento y de decrecimiento. " }}{PARA 0 "
" 0 "" {TEXT 266 5 "Ayuda" }{TEXT -1 17 ": use el comando " }{TEXT 
267 4 "diff" }{TEXT 284 1 " " }{TEXT -1 37 "para derivar la funci\363n
 y el comando " }{TEXT 310 8 "simplify" }{TEXT -1 195 " para simplific
ar la expresi\363n obtenida al derivar.\n.............................
......................................................................
............................................" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "(e) Grafique la funci\363n y la
s as\355ntotas horizontales con el comando " }{TEXT 312 4 "plot" }
{TEXT -1 20 " (utilice la opci\363n " }{TEXT 285 12 "discont=true" }
{TEXT -1 51 " para evitar que MAPLE una las discontinuidades). \n" }}
{PARA 0 "" 0 "" {TEXT 282 1 "4" }{TEXT -1 24 ".- Considere la funci
\363n " }{XPPEDIT 18 0 "g(x) = arcsin(x/(x+1));" "6#/-%\"gG6#%\"xG-%'a
rcsinG6#*&F'\"\"\",&F'F,F,F,!\"\"" }}{PARA 0 "" 0 "" {TEXT -1 192 "(a)
 \277Cu\341l es el dominio de la funci\363n?\n........................
......................................................................
.................................................\n\n(b) \277Es " }
{TEXT 313 1 "g" }{TEXT -1 168 " una funci\363n continua ?\n...........
......................................................................
..............................................................." }}
{PARA 0 "" 0 "" {TEXT -1 219 "\n(c) \277Tiene la funci\363n as\355ntot
as horizontales? En caso afirmativo \277Cu\341les?\n..................
......................................................................
........................................................" }}{PARA 0 "
" 0 "" {TEXT -1 206 "\n(d)Hallar los intervalos de crecimiento y de de
crecimiento.\n........................................................
......................................................................
.................\n " }}{PARA 0 "" 0 "" {TEXT -1 68 "(e) Grafique la f
unci\363n y las as\355ntotas horizontales con el comando " }{TEXT 260 
4 "plot" }{TEXT -1 3 ". \n" }}{PARA 0 "" 0 "" {TEXT 283 1 "5" }{TEXT 
-1 8 ".- Sean " }{TEXT 314 1 "f" }{TEXT -1 3 " y " }{TEXT 315 1 "g" }
{TEXT -1 121 "  las funciones dadas en los dos ejercicios anteriores. \+
Considere la ecuaci\363n f(x) = g(x) y resu\351lvala usando el comando
 " }{TEXT 265 5 "solve" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 
244 "\277Son las soluciones encontradas las \372nicas que hay?  En cas
o afirmativo, \277c\363mo podemos estar seguros?\n....................
......................................................................
...................................................\n" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 1 0" 0 
}{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }