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15 "Introducci\363n" }}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "
" {TEXT 204 11 "1) Calcular" }}{PARA 0 "" 0 "" {TEXT 204 10 "         \+
 " }{XPPEDIT 18 0 "(1+2/(3^4))/5;" "6#*&,&\"\"\"F%*&\"\"#F%*$)\"\"$\"
\"%F%!\"\"F%F%\"\"&F," }{TEXT 204 2 " ." }}{PARA 0 "" 0 "" {TEXT 204 
0 "" }}{PARA 0 "" 0 "" {TEXT 204 14 "2) Calcular   " }{XPPEDIT 18 0 "1
+1/(1+1/(1+1/(1+1/15)));" "6#,&\"\"\"F$*&F$F$,&F$F$*&F$F$,&F$F$*&F$F$,
&F$F$*&F$F$\"#:!\"\"F$F-F$F-F$F-F$" }{TEXT 204 2 " ." }}{PARA 0 "" 0 "
" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 13 "3) Calcular  " }
{XPPEDIT 18 0 "limit((3*n^3+5*n^2-3)/(a*n^3+n), n = infinity);" "6#-%&
limitG6$*&,(*&\"\"$\"\"\"*$)%\"nGF)F*F*F**&\"\"&F**$)F-\"\"#F*F*F*F)!
\"\"F*,&*&%\"aGF*F+F*F*F-F*F3/F-%)infinityG" }{TEXT 204 11 "  , siendo
 " }{XPPEDIT 18 0 "a;" "6#%\"aG" }{TEXT 204 19 " un n\372mero real." }
}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 27 "4) Fac
torizar el n\372mero " }{XPPEDIT 18 0 "1234567890;" "6#\"+!*ycM7" }
{TEXT 204 34 " en producto de n\372meros primos." }}{PARA 0 "" 0 "" 
{TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 34 "5) \277Qu\351 n\372mero
 es mayor, " }{XPPEDIT 18 0 "10^100;" "6#*$)\"#5\"$+\"\"\"\"" }{TEXT 
204 8 "  \363  " }{XPPEDIT 18 0 "factorial(70);" "6#-%*factorialG6#\"#
q" }{TEXT 204 2 " ?" }}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "
" {TEXT 204 48 "6) Obtener, con 4 cifras decimales, el valor de " }
{XPPEDIT 18 0 "sin(Pi/7);" "6#-%$sinG6#*&%#PiG\"\"\"\"\"(!\"\"" }{TEXT
 204 2 ", " }{XPPEDIT 18 0 "exp(5);" "6#-%$expG6#\"\"&" }{TEXT 204 3 "
 y " }{XPPEDIT 18 0 "log(21);" "6#-%$logG6#\"#@" }{TEXT 204 1 "." }}
{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 55 "7) Hall
ar todas las soluciones reales de la ecuaci\363n" }}{PARA 0 "" 0 "" 
{TEXT 204 10 "          " }{XPPEDIT 18 0 "1-2*x+3*x^2-4*x^5 = 0;" "6#/
,*\"\"\"F%*&\"\"#F%%\"xGF%!\"\"*&\"\"$F%*$)F(F'F%F%F%*&\"\"%F%*$)F(\"
\"&F%F%F)\"\"!" }{TEXT 204 1 " " }}{PARA 0 "" 0 "" {TEXT 204 0 "" }
{TEXT 203 0 "" }{TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 55 "8) Hall
ar todas las soluciones reales de la ecuaci\363n" }}{PARA 0 "" 0 "" 
{TEXT 204 10 "          " }{XPPEDIT 18 0 "1-2*x+3*x^2-4*x^5+5*x^6 = 0;
" "6#/,,\"\"\"F%*&\"\"#F%%\"xGF%!\"\"*&\"\"$F%*$)F(F'F%F%F%*&\"\"%F%*$
)F(\"\"&F%F%F)*&F2F%*$)F(\"\"'F%F%F%\"\"!" }{TEXT 204 2 " ." }}{PARA 0
 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 48 "9) Hallar toda
s las soluciones de la ecuaci\363n" }}{PARA 0 "" 0 "" {TEXT 204 10 "  \+
        " }{XPPEDIT 18 0 "2*sin(x)+3*cos(x) = 1;" "6#/,&*&\"\"#\"\"\"-
%$sinG6#%\"xGF'F'*&\"\"$F'-%$cosGF*F'F'F'" }{TEXT 204 2 " ." }}{PARA 0
 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 50 "10) Resolver e
l sistema formado por las ecuaciones" }}{PARA 0 "" 0 "" {TEXT 204 10 "
          " }{XPPEDIT 18 0 "x+2*y+3*z = 4;" "6#/,(%\"xG\"\"\"*&\"\"#F&
%\"yGF&F&*&\"\"$F&%\"zGF&F&\"\"%" }{TEXT 204 1 " " }}{PARA 0 "" 0 "" 
{TEXT 204 10 "          " }{XPPEDIT 18 0 "5*x-6*y+7*z = 8;" "6#/,(*&\"
\"&\"\"\"%\"xGF'F'*&\"\"'F'%\"yGF'!\"\"*&\"\"(F'%\"zGF'F'\"\")" }{TEXT
 204 1 " " }}{PARA 0 "" 0 "" {TEXT 204 10 "          " }{XPPEDIT 18 0 
"9*x+10*y+11*z = 12;" "6#/,(*&\"\"*\"\"\"%\"xGF'F'*&\"#5F'%\"yGF'F'*&
\"#6F'%\"zGF'F'\"#7" }{TEXT 204 1 " " }}{PARA 0 "" 0 "" {TEXT 204 0 ""
 }}{PARA 0 "" 0 "" {TEXT 204 26 "11) Factoriza el polinomio" }}{PARA 0
 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 10 "          " }
{XPPEDIT 18 0 "x^11-34*x^10+520*x^9-4718*x^8+28187*x^7-116288*x^6+3375
64*x^5-688240*x^4+963712*x^3-880128*x^2+470016*x-110592;" "6#,:*$)%\"x
G\"#6\"\"\"F(*&\"#MF(*$)F&\"#5F(F(!\"\"*&\"$?&F(*$)F&\"\"*F(F(F(*&\"%=
ZF(*$)F&\"\")F(F(F.*&\"&(=GF(*$)F&\"\"(F(F(F(*&\"')G;\"F(*$)F&\"\"'F(F
(F.*&\"'kvLF(*$)F&\"\"&F(F(F(*&\"'S#)oF(*$)F&\"\"%F(F(F.*&\"'7P'*F(*$)
F&\"\"$F(F(F(*&\"'G,))F(*$)F&\"\"#F(F(F.*&\"';+ZF(F&F(F(\"'#f5\"F." }
{TEXT 204 1 " " }}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" 
{TEXT 204 32 "12) \277C\372al es el factor de " }{XPPEDIT 18 0 "x^7;" 
"6#*$)%\"xG\"\"(\"\"\"" }{TEXT 204 17 " en el polinomio " }{XPPEDIT 18
 0 "3*(x-5)^10;" "6#*&\"\"$\"\"\"*$),&%\"xGF%\"\"&!\"\"\"#5F%F%" }
{TEXT 204 2 " ?" }}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" 
{TEXT 204 71 "13) Desconponer la siguiente fracci\363n en suma de frac
ciones simples:" }}{PARA 0 "" 0 "" {TEXT 204 10 "          " }
{XPPEDIT 18 0 "(3*x^2+4)/(2*x^4-x^2+x^3+x-3);" "6#*&,&*&\"\"$\"\"\"*$)
%\"xG\"\"#F'F'F'\"\"%F'F',,*&F+F'*$)F*F,F'F'F'F(!\"\"*$)F*F&F'F'F*F'F&
F1F1" }{TEXT 204 3 " . " }}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 ""
 0 "" {TEXT 204 64 "14) Obtener el polinomio de Taylor de orden 4 de l
a funci\363n  " }{XPPEDIT 18 0 "f(x) := x*sen(x);" "6#>-%\"fG6#%\"xG*&
F'\"\"\"-%$senGF&F)" }{TEXT 204 22 "  alrededor del punto " }{XPPEDIT 
18 0 "pi;" "6#%#piG" }{TEXT 204 33 ". Expresarlo como potencias de x."
 }}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 34 "15) \+
Hallar el siguiente l\355mite:" }}{PARA 0 "" 0 "" {TEXT 204 10 "      \+
    " }{XPPEDIT 18 0 "limit((x+x^2*log(1+x)+x^3)^(1/(5+x)), x = infini
ty);" "6#-%&limitG6$),(%\"xG\"\"\"*&)F(\"\"#F)-%$logG6#,&F)F)F(F)F)F)*
$)F(\"\"$F)F)*&F)F),&\"\"&F)F(F)!\"\"/F(%)infinityG" }{TEXT 204 1 " " 
}}{PARA 0 "" 0 "" {TEXT 204 1 " " }}{PARA 0 "" 0 "" {TEXT 204 34 "16) \+
Hallar el siguiente l\355mite:" }}{PARA 0 "" 0 "" {TEXT 204 9 "       \+
  " }{XPPEDIT 18 0 "limit((x+x^2*log(1+x)+x^3)^(1/(5+x)), x = 0, right
);" "6#-%&limitG6%),(%\"xG\"\"\"*&)F(\"\"#F)-%$logG6#,&F)F)F(F)F)F)*$)
F(\"\"$F)F)*&F)F),&\"\"&F)F(F)!\"\"/F(\"\"!%&rightG" }{TEXT 204 1 " " 
}}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 58 "17) D
eterminar si el valor de la derivada de la funci\363n" }}{PARA 0 "" 0 
"" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 14 "              " }
{XPPEDIT 18 0 "f(x) = (x+x^2*log(1+x)+x^3)^(1/(5+x));" "6#/-%\"fG6#%\"
xG),(F'\"\"\"*&)F'\"\"#F*-%$logG6#,&F*F*F'F*F*F**$)F'\"\"$F*F**&F*F*,&
\"\"&F*F'F*!\"\"" }{TEXT 204 4 "    " }}{PARA 0 "" 0 "" {TEXT 204 0 ""
 }}{PARA 0 "" 0 "" {TEXT 204 29 "en el punto x=1 es mayor que " }
{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 204 2 " ." }}
{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 46 "18) Hal
lar la derivada sexta de la funci\363n " }{XPPEDIT 18 0 "f(x) = x*sin(
x)^5;" "6#/-%\"fG6#%\"xG*&F'\"\"\"*$)-%$sinGF&\"\"&F)F)" }{TEXT 204 2 
" ." }}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 12 "
19) Obtener:" }}{PARA 0 "" 0 "" {TEXT 204 10 "          " }{XPPEDIT 18
 0 "sum(k^3+k^2+k+1, k = 1 .. 1000);" "6#-%$sumG6$,**$)%\"kG\"\"$\"\"
\"F+*$)F)\"\"#F+F+F)F+F+F+/F);F+\"%+5" }{TEXT 204 2 " ." }}{PARA 0 "" 
0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 12 "20) Obtener:" }}
{PARA 0 "" 0 "" {TEXT 204 10 "          " }{XPPEDIT 18 0 "sum(1/factor
ial(k), k = 5 .. infinity);" "6#-%$sumG6$*&\"\"\"F'-%*factorialG6#%\"k
G!\"\"/F+;\"\"&%)infinityG" }{TEXT 204 1 " " }}{PARA 0 "" 0 "" {TEXT 
204 0 "" }}{PARA 0 "" 0 "" {TEXT 204 25 "21) Calcular la integral:" }}
{PARA 0 "" 0 "" {TEXT 204 10 "          " }{XPPEDIT 18 0 "int((3*x^2+4
)/(2*x^4-x^2+x^3+x-3), x);" "6#-%$intG6$*&,&*&\"\"$\"\"\"*$)%\"xG\"\"#
F*F*F*\"\"%F*F*,,*&F.F**$)F-F/F*F*F*F+!\"\"*$)F-F)F*F*F-F*F)F4F4F-" }
{TEXT 204 2 " ." }}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" 
{TEXT 204 25 "22) Calcular la integral:" }}{PARA 0 "" 0 "" {TEXT 204 
10 "          " }{XPPEDIT 18 0 "int(cos(x)^4, x = 0 .. Pi/4);" "6#-%$i
ntG6$*$)-%$cosG6#%\"xG\"\"%\"\"\"/F+;\"\"!*&%#PiGF-F,!\"\"" }{TEXT 
204 2 ". " }}{PARA 0 "" 0 "" {TEXT 204 0 "" }}{PARA 0 "" 0 "" {TEXT 
204 42 "23) Dibuja la gr\341fica de la funci\363n:" }}{PARA 0 "" 0 "" 
{TEXT 204 10 "          " }{XPPEDIT 18 0 "f(x) = 1/(x-1);" "6#/-%\"fG6
#%\"xG*&\"\"\"F),&F'F)F)!\"\"F+" }{TEXT 204 2 " ." }}{PARA 0 "" 0 "" 
{TEXT 204 0 "" }}}
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