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{SECT 0 {PARA 257 "" 0 "" {TEXT 259 20 "Bases de Matem\341ticas" }
{TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 261 32 "Soluciones del examen \+
de Maple A" }}{PARA 258 "" 0 "" {TEXT -1 64 "Ingenier\355a T\351cnica \+
en Inform\341tica de Sistemas, de Gesti\363n y LADE" }}{PARA 258 "" 0 
"" {TEXT -1 25 "  1 de Septiembre de 2006" }}{PARA 258 "" 0 "" {TEXT 
-1 0 "" }{TEXT 260 0 "" }{TEXT -1 20 "Duraci\363n: 50 minutos" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
257 0 "" }}{PARA 0 "" 0 "" {TEXT 262 14 "Ejercicio 1:  " }{TEXT 263 
71 "Determinar los intervalos de crecimiento y decrecimiento de la fun
ci\363n." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "f:=x->arctan(x+1)-x;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "solve(diff(f(x),x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 65 "evalf(subs(x=-2,diff(f(x),x)));\nevalf(subs(x=0,diff(
f(x),x)));\n\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f(
x),x=-2..0);" }}}{PARA 0 "" 0 "" {TEXT -1 63 "Siendo su derivada conti
nua, la funci\363n es siempre decreciente." }}{PARA 11 "" 1 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 11 "" 1 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 14 "Ejerci
cio 2:  " }{TEXT -1 45 " Determina un valor del n\372mero real positiv
o " }{XPPEDIT 18 0 "a;" "6#%\"aG" }{TEXT -1 58 " tal que la siguiente \+
funci\363n sea continua en su dominio. " }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 259 "" 0 "" {XPPEDIT 18 0 "f(x) = sin(tan(x)-x)/(tan(x)+1);
" "6#/-%\"fG6#%\"xG*&-%$sinG6#,&-%$tanG6#F'\"\"\"F'!\"\"F0,&-F.6#F'F0F
0F0F1" }{TEXT -1 19 "             si  - " }{XPPEDIT 18 0 "Pi/4;" "6#*&
%#PiG\"\"\"\"\"%!\"\"" }{TEXT -1 3 " < " }{XPPEDIT 18 0 "x <= 0;" "6#1
%\"xG\"\"!" }{TEXT -1 4 ",   " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 259 "" 0 "" {TEXT -1 2 "f(" }{XPPEDIT 18 0 "x;" "6#%\"xG" }
{TEXT -1 7 ") = arc" }{XPPEDIT 18 0 "cos(a+3*x);" "6#-%$cosG6#,&%\"aG
\"\"\"*&\"\"$F(%\"xGF(F(" }{TEXT -1 24 "                si  0 < " }
{XPPEDIT 18 0 "x <= 1;" "6#1%\"xG\"\"\"" }{TEXT -1 1 "." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "Para el valor de " }
{XPPEDIT 18 0 "a;" "6#%\"aG" }{TEXT -1 62 " hallado, determina si la f
unci\363n est\341 acotada en su dominio. " }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve(tan(x)+1,x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "limit(sin(tan(x)-x)/(tan(x)+1), x=0
, left);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "limit(arccos(3*
x+a), x=0,right);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solve(
1/2*Pi-arcsin(a),a);" }}}{PARA 0 "" 0 "" {TEXT -1 164 "Si x es distint
o de 0 la funci\363n es continua, siendo la compuesta de funciones con
tinuas o el cociente de compuestas de funciones continuas con denomina
dor no nulo." }}{PARA 0 "" 0 "" {TEXT -1 73 "Para a=1 la funci\363n es
 continua en x= 0 y, por tanto, en todo su dominio." }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 46 "limit(sin(tan(x)-x)/(tan(x)+1),x=-Pi/4,righ
t);" }}}{PARA 0 "" 0 "" {TEXT -1 53 "La funci\363n tiene como as\355nt
ota vertical la recta x = " }{XPPEDIT 18 0 "-Pi/4;" "6#,$*&%#PiG\"\"\"
\"\"%!\"\"F(" }{TEXT -1 32 "  y, por tanto, no est\341 acotada." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }{TEXT 264 12 "Ejercicio 3:" }{TEXT -1 47 "  D
eterminar el \341rea delimitada por las curvas " }{XPPEDIT 18 0 "g(x) \+
= -5*e^(-2*x);" "6#/-%\"gG6#%\"xG,$*&\"\"&\"\"\")%\"eG,$*&\"\"#F+F'F+!
\"\"F+F1" }{TEXT -1 3 "y  " }{XPPEDIT 18 0 "f(x) = 3*e^(-x);" "6#/-%\"
fG6#%\"xG*&\"\"$\"\"\")%\"eG,$F'!\"\"F*" }}{PARA 0 "" 0 "" {TEXT -1 
16 "con la variable " }{TEXT 265 1 "x" }{TEXT -1 24 " entre 0 y m\341s
 infinito\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "int(3*exp(-x)
+5*exp(-2*x),x=0..infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 
12 "Ejercicio 4:" }{TEXT -1 6 " Sea \{" }{XPPEDIT 18 0 "a[n];" "6#&%\"
aG6#%\"nG" }{TEXT -1 41 "\} la sucesi\363n definida recursivamente por
" }}{PARA 258 "" 0 "" {TEXT -1 0 "" }{XPPEDIT 18 0 "a[1];" "6#&%\"aG6#
\"\"\"" }{TEXT -1 5 " = 45" }}{PARA 258 "" 0 "" {TEXT -1 0 "" }
{XPPEDIT 18 0 "a[n];" "6#&%\"aG6#%\"nG" }{TEXT -1 5 " =   " }{XPPEDIT 
18 0 "abs(2*a[n-1])/3+2;" "6#,&*&-%$absG6#*&\"\"#\"\"\"&%\"aG6#,&%\"nG
F*F*!\"\"F*F*\"\"$F0F*F)F*" }{TEXT -1 13 "             " }{XPPEDIT 18 
0 "2 <= n;" "6#1\"\"#%\"nG" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
118 "Determinar una aproximaci\363n al l\355mite de esta sucesi\363n, \+
cuyo error de aproximaci\363n sea del orden de las diezmil\351simas." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "La suce
si\363n es contractiva y su constante es C=2/3." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart;\n2*
45/3+2-45;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 37 "cota:=subs(c=2/3,c^(n-1)/(1-c)*(13));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "i:=1:\nwhile abs(subs(n=i,cota))>10
^(-4) do\n   i:=i+1:\nod:\ni;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "54" 0 }{VIEWOPTS 1 
1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }