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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 58 "Ingenier\355a T\351cnica \+
en Inform\341tica de Sistemas, de Gesti\363n " }}{PARA 258 "" 0 "" 
{TEXT -1 21 " 8 de Febrero de 2006" }}{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 13 "Ejercicio 1: " }{TEXT 264 62 "Hallar exactamente el \341
rea de la regi\363n limitada por la recta " }{XPPEDIT 18 0 "x = 2;" "6
#/%\"xG\"\"#" }{TEXT 266 14 " y las curvas " }{XPPEDIT 18 0 "g(x) = x^
4-x^3+x-1;" "6#/-%\"gG6#%\"xG,**$F'\"\"%\"\"\"*$F'\"\"$!\"\"F'F+F+F." 
}}{PARA 0 "" 0 "" {TEXT -1 2 "y " }{XPPEDIT 18 0 "g(x) = -x^3+x;" "6#/
-%\"gG6#%\"xG,&*$F'\"\"$!\"\"F'\"\"\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT 265 1 " " }{TEXT 263 1 " " }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 26 "solve(x^4-x^3+x-1=-x^3+x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 132 "with(plots):\nplot1:=plot(x^4-x^3+
x-1,x=-2..2,colour=red):\nplot2:=plot(-x^3+x,x=-2..2,colour=green):\np
lots[display](\{plot1,plot2\});\n\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 70 "int(-x^3+x-(x^4-x^3+x-1),x=-1..1)+int(-(-x^3+x)+(x^4-
x^3+x-1),x=1..2);" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }{TEXT 259 14 "Ejercicio 2:  " }{TEXT -1 53 " Determin
a para qu\351 valores del n\372mero real positivo " }{XPPEDIT 18 0 "a;
" "6#%\"aG" }{TEXT -1 49 " la siguiente funci\363n es continua en su d
ominio. " }}{PARA 259 "" 0 "" {XPPEDIT 18 0 "f(x) = (exp(x)-a)/x;" "6#
/-%\"fG6#%\"xG*&,&-%$expG6#F'\"\"\"%\"aG!\"\"F-F'F/" }{TEXT -1 30 "   \+
                       si  " }{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 
8 " < 0,   " }}{PARA 259 "" 0 "" {TEXT -1 2 "f(" }{XPPEDIT 18 0 "x;" "
6#%\"xG" }{TEXT -1 47 ") = 1                                     si   \+
" }{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 8 " = 0,   " }}{PARA 259 "" 
0 "" {TEXT -1 2 "f(" }{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 4 ") = " 
}{XPPEDIT 18 0 "(tan(x+Pi/4)-x)/(x+a);" "6#*&,&-%$tanG6#,&%\"xG\"\"\"*
&%#PiGF*\"\"%!\"\"F*F*F)F.F*,&F)F*%\"aGF*F." }{TEXT -1 17 "           \+
 si   " }{XPPEDIT 18 0 "0 < x;" "6#2\"\"!%\"xG" }{TEXT -1 3 " < " }
{XPPEDIT 18 0 "Pi/4;" "6#*&%#PiG\"\"\"\"\"%!\"\"" }{TEXT -1 1 "," }}
{PARA 0 "" 0 "" {TEXT -1 22 "Para estos valores de " }{XPPEDIT 18 0 "a
;" "6#%\"aG" }{TEXT -1 61 " halla, si existen, sus as\355ntotas vertic
ales y horizontales. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 41 "restart:limit((exp(x)-a)/(x), x=0, left);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "limit((tan(x+Pi/4)-x)/(
x+a),x=0,right);" }}}{PARA 0 "" 0 "" {TEXT -1 41 "Si x = 0 la funci
\363n es continua s\363lo si  " }{XPPEDIT 18 0 "a = 1;" "6#/%\"aG\"\"
\"" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "a:=1;l
imit((exp(x)-a)/(x), x=0, left);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 
"limit((tan(x+Pi/4)-x)/(x+a),x=0,right);" }}}{PARA 0 "" 0 "" {TEXT -1 
156 "Si x es distinto de 0 y a=1, la funci\363n es continua  en su dom
inio (es un cociente de funciones compuestas de funciones continuas, c
on denominador no nulo)." }}{PARA 0 "" 0 "" {TEXT -1 70 "Tiene as\355n
totas verticales cada vez que las tiene la tangente: en x = " }
{XPPEDIT 18 0 "Pi/4;" "6#*&%#PiG\"\"\"\"\"%!\"\"" }{TEXT -1 1 "." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "limit((tan(x+Pi/4)-x)/(x+a),
x=Pi/4, left);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "limit((ex
p(x)-a)/x,x=-infinity);" }}}{PARA 0 "" 0 "" {TEXT -1 10 "La recta  " }
{XPPEDIT 18 0 "y = 0;" "6#/%\"yG\"\"!" }{TEXT -1 27 " es un as\355ntot
a horizontal." }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 256 12 "Ejercicio 3:" }{TEXT -1 73 "  Determinar \+
los intervalos de crecimiento y decrecimiento de la funci\363n " }
{XPPEDIT 18 0 "f(x) = 3^x-2^x;" "6#/-%\"fG6#%\"xG,&)\"\"$F'\"\"\")\"\"
#F'!\"\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 116 "Digits:=15:f:=x->3^x-2^x:\nevalf(solve(diff(f(x),x))
);\nevalf(subs(x=-2,diff(f(x),x)));\nevalf(subs(x=0,diff(f(x),x)));" }
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 76 "Decrece
 desde menos infinito hasta el punto cr\355tico y a partir de ah\355 c
rece." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 12 
"Ejercicio 4:" }{TEXT -1 43 " Trabajamos con 15 decimales exactos. Sea
 \{" }{XPPEDIT 18 0 "a[n];" "6#&%\"aG6#%\"nG" }{TEXT -1 41 "\} la suce
si\363n definida recursivamente por" }}{PARA 258 "" 0 "" {TEXT -1 0 "
" }{XPPEDIT 18 0 "a[1];" "6#&%\"aG6#\"\"\"" }{TEXT -1 6 " = -23" }}
{PARA 258 "" 0 "" {TEXT -1 0 "" }{XPPEDIT 18 0 "a[n];" "6#&%\"aG6#%\"n
G" }{TEXT -1 5 " =   " }{XPPEDIT 18 0 "10*abs(a[n-1])/37+2;" "6#,&*(\"
#5\"\"\"-%$absG6#&%\"aG6#,&%\"nGF&F&!\"\"F&\"#PF/F&\"\"#F&" }{TEXT -1 
13 "             " }{XPPEDIT 18 0 "2 <= n;" "6#1\"\"#%\"nG" }{TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "Ca
lcular el t\351rmino 124 de la sucesi\363n. Construir el primer t\351r
mino de la sucesion " }{XPPEDIT 18 0 "\{b[n] = -a[n+1]+a[n]\};" "6#<#/
&%\"bG6#%\"nG,&&%\"aG6#,&F(\"\"\"F.F.!\"\"&F+6#F(F." }}{PARA 0 "" 0 "
" {TEXT -1 45 "que, en valor absoluto, sea menor que 10^\{-4\}" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
72 "Digits:=15:\na:=proc(n)\nif n=1 then -23\nelse abs(10*a(n-1))/37+2
 fi:\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(a(124))
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "b:=proc(n)\nif n=1 the
n -a(2)+a(1)\nelse 27*a(n)/37-2 fi:\nend:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 52 "n:=1:\nwhile abs(b(n))>=10^(-4) do \n  n:=n+1: \nod
:\nn;" }}}}{MARK "48" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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