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{SECT 0 {PARA 257 "" 0 "" {TEXT 260 20 "Bases de Matem\341ticas" }
{TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 262 32 "Soluciones del examen \+
de Maple C" }}{PARA 258 "" 0 "" {TEXT -1 59 "Ingenier\355a T\351cnica \+
en Inform\341tica de Sistemas y de Gesti\363n " }}{PARA 258 "" 0 "" 
{TEXT -1 21 " 5 de Febrero de 2007" }}{PARA 258 "" 0 "" {TEXT -1 0 "" 
}{TEXT 261 0 "" }{TEXT -1 20 "Duraci\363n: 50 minutos" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 258 14 "Ejercicio 1:  " }{TEXT -1 58 "Estudiar si la ra\355z cua
rta de  123  es mayor o menor que  " }{TEXT 263 0 "" }{XPPEDIT 18 0 "P
i;" "6#%#PiG" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 260 "" 1 "" {TEXT 268 9 "Soluci\363n:" }{TEXT -1 6 " Como:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "evalf((123)^(1/4))-evalf(Pi)
;" }}}{PARA 0 "" 0 "" {TEXT -1 50 "tenemos que  la ra\355z cuarta de 1
23  es mayor que  " }{TEXT 265 0 "" }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }
{TEXT -1 2 " ." }{TEXT 264 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 259 14 "Ejercicio 2:  " }{TEXT 
-1 88 "Determinar los extremos relativos (determinando si son m\341xim
os o m\355nimos) de la funci\363n " }}{PARA 258 "" 0 "" {TEXT -1 7 "F(
x) = " }{XPPEDIT 18 0 "x^6+3*x^5+3*x^2-x+1.;" "6#,,*$%\"xG\"\"'\"\"\"*
&\"\"$F'*$F%\"\"&F'F'*&F)F'*$F%\"\"#F'F'F%!\"\"-%&FloatG6$F'\"\"!F'" }
{TEXT -1 0 "" }}{PARA 260 "" 1 "" {TEXT 269 9 "Soluci\363n:" }{TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "F:=x->x^6+3*x^5+3*
x^2-x+1;" }}}{PARA 0 "" 0 "" {TEXT -1 29 "Derivamos e igualamos a cero
:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "evalf(solve(diff(F(x),x
),x));" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 
"El punto " }{XPPEDIT 18 0 "-2.425062753;" "6#,$-%&FloatG6$\"+`F1DC!\"
*!\"\"" }{TEXT -1 27 " es un m\355nimo relativo, el " }{XPPEDIT 18 0 "
-.9055676555;" "6#,$-%&FloatG6$\"+blnb!*!#5!\"\"" }{TEXT -1 27 " es un
 m\341ximo relativo, el " }{XPPEDIT 18 0 ".1647056416;" "6#-%&FloatG6$
\"+;k0Z;!#5" }{TEXT -1 64 "  es un m\355nimo relativo, como se aprecia
 a continuaci\363n:        " }}{PARA 0 "" 0 "" {TEXT -1 7 "       " }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(F(x),x=-3..-2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(F(x),x=-1..0);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(F(x),x=0..1);" }}}
{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
256 12 "Ejercicio 3:" }{TEXT -1 6 "  Sea " }{XPPEDIT 18 0 "\{a[n]\};" 
"6#<#&%\"aG6#%\"nG" }{TEXT -1 48 " la sucesi\363n definida, para todo \+
n\372mero natural " }{TEXT 270 1 "n" }{TEXT -1 6 ", por " }{XPPEDIT 
18 0 "a[n] = cos(Pi/2+(-1)^n*((n+1)/n)^n);" "6#/&%\"aG6#%\"nG-%$cosG6#
,&*&%#PiG\"\"\"\"\"#!\"\"F.*&),$F.F0F'F.)*&,&F'F.F.F.F.F'F0F'F.F." }
{TEXT -1 61 ". Si la sucesi\363n converge, halla su l\355mite. (Se rec
uerda que " }{XPPEDIT 18 0 "cos(Pi/2+x) = -sin(x);" "6#/-%$cosG6#,&*&%
#PiG\"\"\"\"\"#!\"\"F*%\"xGF*,$-%$sinG6#F-F," }{TEXT -1 7 " y que " }
{XPPEDIT 18 0 "sin(-x) = (-sin)(x);" "6#/-%$sinG6#,$%\"xG!\"\"-,$F%F)6
#F(" }{TEXT -1 2 ")." }}{PARA 260 "" 1 "" {TEXT 266 9 "Soluci\363n:" }
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "restart;a:=n
->cos(Pi/2+((-1)^n)*((n+1)/n)^n);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "seq(a(n),n=1..200):" }}}{PARA 0 "" 0 "" {TEXT -1 0 "
" }{TEXT 271 38 "Representaci\363n gr\341fica de la sucesi\363n:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "n:=`n`:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 43 "plot([seq([n,a(n)],n=1..200)],style=point);" 
}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 272 19 "C\341lculo del l\355mi
te:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "n:=`n`:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Limit(a(n),n=infinity)=limit(a(n),n
=infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "b:=n->((-1)^
n)*((n+1)/n)^n;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Limit(b(
n),n=infinity)=limit(b(n),n=infinity);" }}}{PARA 0 "" 0 "" {TEXT -1 
192 "La sucesion b est\341 formada por dos subsucesiones convergentes \+
a l\355mites distintos: una, la de los t\351rminos pares, converge al \+
n\372mero e y la otra, la de los t\351rminos impares, a su opuesto (-e
)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "Limit(a(n),n=infinity)=limit(-sin(b(n)),n=infinity);
" }}}{PARA 0 "" 0 "" {TEXT -1 112 "La sucesi\363n dada converger\341 p
or un lado ,en sus t\351rminos pares, a -sen(e) y por otro,en los impa
res, a -sen(-e) " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "sin(exp(
1));sin(-exp(1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "sin(ex
p(1))-sin(-exp(1));" }}}{PARA 0 "" 0 "" {TEXT -1 41 "ambos l\355mites \+
son distintos y por tanto. " }{TEXT 273 39 "La sucesi\363n dada no es \+
es convergente. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 12 "Ejerc
icio 4:" }{TEXT -1 59 " Hallar el \341rea encerrada por la gr\341fica \+
de las funciones  " }{XPPEDIT 18 0 "f(x) = sec(Pi*x/3)^2;" "6#/-%\"fG6
#%\"xG*$-%$secG6#*(%#PiG\"\"\"F'F.\"\"$!\"\"\"\"#" }{TEXT -1 4 " y  " 
}{XPPEDIT 18 0 "g(x) = x^(1/3);" "6#/-%\"gG6#%\"xG)F'*&\"\"\"F*\"\"$!
\"\"" }{TEXT -1 10 " en [0,1]." }}{PARA 260 "" 1 "" {TEXT 267 9 "Soluc
i\363n:" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "re
start:with(plots):f:=x->(1/cos(Pi*x/3))^2;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 14 "g:=x->x^(1/3);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "plot(\{f(x),g(x)\},x=0..1);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 10 "f(0)-g(0);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "A:=int(f(x)-g(x),x=0..1);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "11 0" 31 }{VIEWOPTS 1 
1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }