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}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 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$" }{TEXT 214 2 " ." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "1+1/(1+1/(1+1/(1+1/15)));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#y\"#Z" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 13 "3) Calcular " }{XPPEDIT 18 0 "limit((3*n^3+5*n^2-3)/(a*n^3+n), n \+ = infinity);" "6#-%&limitG6$*&,(*&\"\"$\"\"\"*$)%\"nGF)F*F*F**&\"\"&F* *$)F-\"\"#F*F*F*F)!\"\"F*,&*&%\"aGF*F+F*F*F-F*F3/F-%)infinityG" }{TEXT 214 11 " , siendo " }{XPPEDIT 18 0 "a;" "6#%\"aG" }{TEXT 214 19 " un n\372mero real." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "limit((3*n^3+5*n^2-3)/(a*n^3+n),n = infinity) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"$\"\"\"F&F&%\"aG!\"\"F&" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 200 15 "Obse rvaci\363n:" }}{PARA 0 "" 0 "" {TEXT 214 31 "La respuesta correcta ser \355a " }{XPPEDIT 18 0 "3/a;" "6#*&\"\"$\"\"\"%\"aG!\"\"" }{TEXT 214 4 " si " }{XPPEDIT 18 0 "a;" "6#%\"aG" }{TEXT 214 16 " es distinto de \+ " }{XPPEDIT 18 0 "0;" "6#\"\"!" }{TEXT 214 4 ", e " }{XPPEDIT 18 0 "in finity;" "6#%)infinityG" }{TEXT 214 4 " si " }{XPPEDIT 18 0 "a = 0;" " 6#/%\"aG\"\"!" }{TEXT 214 1 "." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 27 "4) Fact orizar el n\372mero " }{XPPEDIT 18 0 "1234567890;" "6#\"+!*ycM7" } {TEXT 214 34 " en producto de n\372meros primos." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "ifactor(123 4567890);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*,-%!G6#\"\"#\"\"\")-F%6# \"\"$F'F(-F%6#\"\"&F(-F%6#\"%.QF(-F%6#\"%2OF(" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 34 "5) \277Qu\351 n\372mero es mayor, " }{XPPEDIT 18 0 "10^1 00;" "6#*$)\"#5\"$+\"\"\"\"" }{TEXT 214 8 " \363 " }{XPPEDIT 18 0 "f actorial(70);" "6#-%*factorialG6#\"#q" }{TEXT 214 2 " ?" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "(10^10 0)/(70!);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"`o++++++++++++++++]7Gj BnEXphhi+&)4#*3W%\"`o\"Rvvrq!40z6tO`" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Q2C[$)!#5" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 17 " Luego, es mayor " }{XPPEDIT 18 0 "facto rial(70);" "6#-%*factorialG6#\"#q" }{TEXT 214 11 " . " }} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 48 "6) Obtener, con 4 cifras decimales, el v alor de " }{XPPEDIT 18 0 "sin(Pi/7);" "6#-%$sinG6#*&%#PiG\"\"\"\"\"(! \"\"" }{TEXT 214 2 ", " }{XPPEDIT 18 0 "exp(5);" "6#-%$expG6#\"\"&" } {TEXT 214 3 " y " }{XPPEDIT 18 0 "log(21);" "6#-%$logG6#\"#@" }{TEXT 214 1 "." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "evalf(sin(Pi/7)); evalf(exp(5)); evalf(log(21));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+$RP)QV!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+\"fJT[\"!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" +QC_WI!\"*" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 105 "O, tambi\351n, para los dos \372ltimos casos (observandose ta mbi\351n porqu\351 no sirve para el primero)" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "sin(Pi/(7.)); exp (5.); log(21.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#,$*&$\"+H9 dG9!#5\"\"\"%#PiGF+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+\"fJT[\"! \"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+QC_WI!\"*" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 40 "Luego, el resultado \+ es, respectivamente," }}{PARA 0 "" 0 "" {TEXT 214 16 " 0,4338 " }}{PARA 0 "" 0 "" {TEXT 214 18 " 148,4131" }}{PARA 0 "" 0 " " {TEXT 214 16 " 3,0445" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 55 "7) Hall ar todas las soluciones reales de la ecuaci\363n" }}{PARA 0 "" 0 "" {TEXT 214 10 " " }{XPPEDIT 18 0 "1-2*x+3*x^2-4*x^5 = 0;" "6#/ ,*\"\"\"F%*&\"\"#F%%\"xGF%!\"\"*&\"\"$F%*$)F(F'F%F%F%*&\"\"%F%*$)F(\" \"&F%F%F)\"\"!" }{TEXT 214 1 " " }}{PARA 0 "" 0 "" {TEXT 214 0 "" } {TEXT 204 0 "" }{TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "fsolve(1-2*x+3*x^2-4*x^5=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+ya6 \+ " 0 "" {MPLTEXT 1 0 36 "fsolve(1-2*x+3*x^2-4*x^5+5*x^6=0,x);" }}} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 3 "No " } {TEXT 205 8 "\"sale\"" }{TEXT 214 13 " nada porque " }{TEXT 206 2 "no" }{TEXT 214 69 " hay raices reales. esto tambi\351n se observa de la s iguiente forma:" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 35 "solve(1-2*x+3*x^2-4*x^5+5*x^6=0,x);" }}{PARA 200 "" 1 "" {XPPMATH 20 "6(-%'RootOfG6$,,\"\"\"F'*&\"\"#F'%#_ZGF'!\"\" *&\"\"$F')F*F)F'F'*&\"\"%F')F*\"\"&F'F+*&F2F')F*\"\"'F'F'/%&indexGF'-F $6$F&/F7F)-F$6$F&/F7F--F$6$F&/F7F0-F$6$F&/F7F2-F$6$F&/F7F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 200 "" 1 "" {XPPMATH 20 "6(,&$\"+3XWjy!#5\"\"\"*&$\"+B4SRXF&F'^#F'F'F',&$\"+6R]#p# F&F'*&$\"+/(*)[%[F&F'F+F'F',&$\"+>%[fb'F&!\"\"*&$\"+eJs)*fF&F'F+F'F',& F3F5F6F5,&F-F'F/F5,&F$F'F(F5" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 48 "9) Hall ar todas las soluciones de la ecuaci\363n" }}{PARA 0 "" 0 "" {TEXT 214 10 " " }{XPPEDIT 18 0 "2*sin(x)+3*cos(x) = 1;" "6#/,&*&\" \"#\"\"\"-%$sinG6#%\"xGF'F'*&\"\"$F'-%$cosGF*F'F'F'" }{TEXT 214 2 " ." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "_EnvAllSolutions := true:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(2*sin(x)+3*cos(x)=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&-%'arctanG6#*&,&#\"\"#\"#8\"\"\"*&#\"\"'F+F,*$-%%sqrt G6#\"\"$F,F,!\"\"F,,&#F4F+F,*&#\"\"%F+F,F1F,F,F5F,*(F*F,%#PiGF,%%_Z1|i rGF,F,,(-F%6#*&,&F)F,*&F.F,F1F,F,F,,&F7F,*&F9F,F0F,F5F5F,F " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&$\"+=#)e " 0 "" {MPLTEXT 1 0 18 "e1:=x+2* y+3*z=4;\n" }{MPLTEXT 1 0 20 "e2:=5*x-6*y+7*z=8;\n" }{MPLTEXT 1 0 23 " e3:=9*x+10*y+11*z=12;\n" }{MPLTEXT 1 0 20 "solve(\{e1,e2,e3\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e1G/,(%\"xG\"\"\"*&\"\"#F(%\"yGF(F( *&\"\"$F(%\"zGF(F(\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e2G/,(*& \"\"&\"\"\"%\"xGF)F)*&\"\"'F)%\"yGF)!\"\"*&\"\"(F)%\"zGF)F)\"\")" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e3G/,(*&\"\"*\"\"\"%\"xGF)F)*&\"#5F )%\"yGF)F)*&\"#6F)%\"zGF)F)\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/ %\"xG#!\"\"\"\"#/%\"zG#\"\"$F(/%\"yG\"\"!" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 26 "11) Factoriza el polinomio" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 10 " " }{XPPEDIT 18 0 "x^11-34*x^10 +520*x^9-4718*x^8+28187*x^7-116288*x^6+337564*x^5-688240*x^4+963712*x^ 3-880128*x^2+470016*x-110592;" "6#,:*$)%\"xG\"#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 214 1 " " }}{PARA 0 " " 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "factor(x^11-34*x^10+520*x^9-4718*x^8+281 87*x^7-116288*x^6+337564*x^5-688240*x^4+963712*x^3-880128*x^2+470016*x -110592);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**,&%\"xG\"\"\"F&!\"\"F&) ,&F%F&\"\"#F'F*F&),&F%F&\"\"$F'F-F&),&F%F&\"\"%F'\"\"&F&" }}}{PARA 0 " " 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 32 "12) \277C\372al es el factor de " }{XPPEDIT 18 0 "x^7 ;" "6#*$)%\"xG\"\"(\"\"\"" }{TEXT 214 17 " en el polinomio " } {XPPEDIT 18 0 "3*(x-5)^10;" "6#*&\"\"$\"\"\"*$),&%\"xGF%\"\"&!\"\"\"#5 F%F%" }{TEXT 214 2 " ?" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "expand(3*(x-5)^10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,8*&\"\"$\"\"\")%\"xG\"#5F&F&*&\"$]\"F&)F(\"\"*F&! \"\"*&\"%vLF&)F(\"\")F&F&*&\"&+]%F&)F(\"\"(F&F.*&\"']PRF&)F(\"\"'F&F&* &\"(+DO#F&)F(\"\"&F&F.*&\"(]P%)*F&)F(\"\"%F&F&*&\")+]7GF&)F(F%F&F.*&\" )vVt_F&)F(\"\"#F&F&*&\")]PfeF&F(F&F.\")voHHF&" }}}{PARA 0 "" 0 "" {TEXT 214 6 " " }}{PARA 0 "" 0 "" {TEXT 214 39 "Luego, el coefici ente pedido es -45000." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 71 "13) Desconponer la siguiente fracci\363n en suma de fracciones simples:" }}{PARA 0 "" 0 "" {TEXT 214 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 214 3 " . " }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "convert((3*x^2+4)/(2*x^4-x^2+x^3+x-3), parfra c,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*(#\"\"(\"#5\"\"\"F(F(,&%\" xGF(F(!\"\"F+F(*&#\"#')\"#lF(*&F(F(,&*&\"\"#F(F*F(F(\"\"$F(F+F(F+*&#F( \"#EF(*&,&\"\"&F(F*F(F(,&*$)F*F3F(F(F(F(F+F(F+" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 64 "14) Obtener el polinomio de Taylor de orden 4 de la func i\363n " }{XPPEDIT 18 0 "f(x) := x*sen(x);" "6#>-%\"fG6#%\"xG*&F'\"\" \"-%$senGF&F)" }{TEXT 214 22 " alrededor del punto " }{XPPEDIT 18 0 " pi;" "6#%#piG" }{TEXT 214 33 ". Expresarlo como potencias de x." }} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "taylor(x*sin(x),x=Pi,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+-,& %\"xG\"\"\"%#PiG!\"\",$F'F(F&F(\"\"#,$*&#F&\"\"'F&F'F&F&\"\"$F-\"\"%-% \"OG6#F&\"\"&" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "convert(%, polynom);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&%#PiG\"\"\",&% \"xGF&F%!\"\"F&F)*$)F'\"\"#F&F)*(#F&\"\"'F&F%F&)F'\"\"$F&F&*&F.F&)F'\" \"%F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,.*&%#PiG\"\"\"%\"xGF&F&*$)F'\"\"#F&! \"\"*&#F&F*F&*&F%F&)F'\"\"$F&F&F+*(F-F&)F%F*F&F)F&F&*&#F&\"\"'F&*&F'F& )F%F0F&F&F+*&F4F&)F'\"\"%F&F&" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 34 "15) Hal lar el siguiente l\355mite:" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 10 " " }{XPPEDIT 18 0 "limit((x+x^2*log(1 +x)+x^3)^(1/(5+x)), x = infinity);" "6#-%&limitG6$),(%\"xG\"\"\"*&)F( \"\"#F)-%$logG6#,&F)F)F(F)F)F)*$)F(\"\"$F)F)*&F)F),&\"\"&F)F(F)!\"\"/F (%)infinityG" }{TEXT 214 1 " " }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "limit((x+x^2*log(1+x)+x^3)^( 1/(5+x)), x=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 1 " " }} {PARA 0 "" 0 "" {TEXT 214 34 "16) Hallar el siguiente l\355mite:" }} {PARA 0 "" 0 "" {TEXT 214 9 " " }{XPPEDIT 18 0 "limit((x+x^2*l og(1+x)+x^3)^(1/(5+x)), x = 0, right);" "6#-%&limitG6%),(%\"xG\"\"\"*& )F(\"\"#F)-%$logG6#,&F)F)F(F)F)F)*$)F(\"\"$F)F)*&F)F),&\"\"&F)F(F)!\" \"/F(\"\"!%&rightG" }{TEXT 214 1 " " }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "limit((x+x^2*log(1+x)+x^3) ^(1/(5+x)), x=0, right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 58 "17) Determinar si el valor de la derivad a de la funci\363n" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 14 " " }{XPPEDIT 18 0 "f(x) = (x+x^2*log(1+x)+ x^3)^(1/(5+x));" "6#/-%\"fG6#%\"xG),(F'\"\"\"*&)F'\"\"#F*-%$logG6#,&F* F*F'F*F*F**$)F'\"\"$F*F**&F*F*,&\"\"&F*F'F*!\"\"" }{TEXT 214 4 " " }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 29 "en el punto x=1 es mayor que " }{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#!\" \"" }{TEXT 214 2 " ." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f:=x->(x+x^2*log(1+x)+x^3)^(1/(5+x));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrow GF(),(F'\"\"\"*&)F'\"\"#F.-%$logG6#,&F'F.F.F.F.F.*$)F'\"\"$F.F.*&F.F., &\"\"&F.F'F.!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D (f)(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&),&\"\"#\"\"\"-%#lnG6#F&F '#F'\"\"'F',&*&#F'\"#OF'-F)6#F%F'!\"\"*(F+F',&#\"\"*F&F'*&F&F'F(F'F'F' F%F3F'F'" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+88:s R!#5" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 23 "Luego, no es mayor que " }{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#! \"\"" }{TEXT 214 2 " ." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 46 "18) Hallar la deri vada sexta de la funci\363n " }{XPPEDIT 18 0 "f(x) = x*sin(x)^5;" "6#/ -%\"fG6#%\"xG*&F'\"\"\"*$)-%$sinGF&\"\"&F)F)" }{TEXT 214 2 " ." }} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "D6(f)(x):=diff(x*sin(x)^5, x$6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>--%#D6G6#%\"fG6#%\"xG,.*&\"$?(\"\"\")-%$cosGF)\"\"&F.F.*(\"&+3\"F .)-%$sinGF)\"\"#F.)F0\"\"$F.!\"\"*(\"%IsF.)F6\"\"%F.F0F.F.**\"%+UF.F*F .F6F.)F0F?F.F;**\"&?-\"F.F*F.)F6F:F.)F0F8F.F.*(\"%07F.F*F.)F6F2F.F;" } }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 12 "19) Obtener:" }}{PARA 0 "" 0 "" {TEXT 214 10 " " }{XPPEDIT 18 0 "sum(k^3+k^2+k+1, k = 1 .. 1000);" "6#-%$sumG6$,**$)%\"kG\"\"$\"\"\"F+*$)F)\"\"#F+F+F)F+F+F+/F);F+\"%+5" }{TEXT 214 2 " ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "sum(k^3+ k^2+k+1,k = 1 .. 1000);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"-+]eM3D" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 12 "20) Obtener:" }}{PARA 0 "" 0 "" {TEXT 214 10 " " } {XPPEDIT 18 0 "sum(1/factorial(k), k = 5 .. infinity);" "6#-%$sumG6$*& \"\"\"F'-%*factorialG6#%\"kG!\"\"/F+;\"\"&%)infinityG" }{TEXT 214 1 " \+ " }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "sum(1/k!,k = 5 .. infinity); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(#\"\"\"\"#CF&-%$expG6#F&F&,&F'F&*&\"#lF&-F)6#!\"\"F&F0F&F&" }} }{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }} {PARA 0 "" 0 "" {TEXT 214 25 "21) Calcular la integral:" }}{PARA 0 "" 0 "" {TEXT 214 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 214 2 " ." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "int((3*x^2+4)/(2*x^4-x^2+x^3+x-3),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&#\"\"(\"#5\"\"\"-%#lnG6#,&%\"xGF(F(!\"\"F(F(*& #\"#V\"#lF(-F*6#,&*&\"\"#F(F-F(F(\"\"$F(F(F.*&#F(\"#_F(-F*6#,&*$)F-F7F (F(F(F(F(F.*&#\"\"&\"#EF(-%'arctanG6#F-F(F." }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 25 "22) Calcular la integral:" }}{PARA 0 "" 0 "" {TEXT 214 10 " \+ " }{XPPEDIT 18 0 "int(cos(x)^4, x = 0 .. Pi/4);" "6#-%$intG6$*$)-%$ cosG6#%\"xG\"\"%\"\"\"/F+;\"\"!*&%#PiGF-F,!\"\"" }{TEXT 214 2 ". " }} {PARA 0 "" 0 "" {TEXT 214 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "int((cos(x))^4,x = 0 .. Pi/4);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&#\"\"\"\"\"%F%*&#\"\"$\"#KF %%#PiGF%F%" }}}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 42 "23) Dibuja la gr\341fica de l a funci\363n:" }}{PARA 0 "" 0 "" {TEXT 214 10 " " }{XPPEDIT 18 0 "f(x) = 1/(x-1);" "6#/-%\"fG6#%\"xG*&\"\"\"F),&F'F)F)!\"\"F+" } {TEXT 214 2 " ." }}{PARA 0 "" 0 "" {TEXT 214 0 "" }}{PARA 0 "" 0 "" {TEXT 214 23 "Notemos que si hacemos:" }}{PARA 0 "" 0 "" {TEXT 214 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->1/(1-x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*& \"\"\"F-,&F-F-F'!\"\"F/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "plot(f);" }}{PARA 13 "" 1 "" {TEXT 217 0 "" }{GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%+AXESLABELSG6$Q!6\"F&-%'CURVESG6$7jp7$$!#5\"\"!$ \"3;\"4444444*!#>7$$!3!pmmm\"p0k&*!#<$\"3U?kF?.1m%*F27$$!3uKL$32\"FC7$$!3OLL$3i.9!zF6$\"3%pc\"3J$=M7\"FC7$$!3fmm;/R=0v F6$\"3u%)=;INvv6FC7$$!3k++]P8#\\4(F6$\"3.A[BbCMN7FC7$$!3Kmm;/siqmF6$\" 3C96aeVn.8FC7$$!3Q****\\(y$pZiF6$\"3Kp@oS#\\(z8FC7$$!3jKLL$yaE\"eF6$\" 3apw$ybcyY\"FC7$$!3s%HaF6$\"3K1RmBwLb:FC7$$!3]******\\$*4)*\\F6 $\"3!o*pH#z%>n;FC7$$!3o******\\_&\\c%F6$\"33Fm6V'fpz\"FC7$$!3%)****** \\1aZTF6$\"3`]$Q^GvE%>FC7$$!3Imm;/#)[oPF6$\"39OoH525(4#FC7$$!3%HLLL=ex J$F6$\"3^g!)H'o;gJ#FC7$$!3lKLLL2$f$HF6$\"3ZnEE=^pSDFC7$$!3%)****\\PYx \"\\#F6$\"3m*o4fDtQ'GFC7$$!3gLLLL7i)4#F6$\"3#e:&y5=CFKFC7$$!3o)***\\P' psm\"F6$\"39p1&RE_\"\\PFC7$$!3?****\\74_c7F6$\"3JFJr_3gJWFC7$$!3M:LL$3 x%z#)FC$\"398zt5ghqaFC7$$!3()HLL3s$QM%FC$\"3%)o5=t^jrpFC7$$!3>****\\iv F@AFC$\"3?3]@11X#=)FC7$$!3]^omm;zr)*!#?$\"3=!R'zzqC-**FC7$$\"3aPL$3-Dg 5#FC$\"3W$*)R^\"*)ym7F67$$\"3fVLLezw5VFC$\"3kvVXvkqd7ADl#F67$$\"3u0+vo>\")4nFC $\"3!\\fsB(*R$RIF67$$\"3=QL$3x?'*=(FC$\"3WL/+_'Q#eNF67$$\"3R/](=/wP+zy#) FC$\"3`zYVUk')4eF67$$\"3=P3_+&=kWRoF67$$\"3Mr;/E]Wn')FC$\"3uA)y)G3Q/vF67$$\"3%y3-))o'*p z)FC$\"3ow^it!HDJ)F67$$\"3[0Dc^$[l#*)FC$\"3&3+=$)HVdJ*F67$$\"37BHK9+5c !*FC$\"3I*4!=yUVf5!#;7$$\"3iRL3x;l&=*FC$\"3XrL4fd(zA\"Fby7$$\"3:cP%)RL ?:$*FC$\"3_D?\"e\\(Gg9Fby7$$\"3ytTg-]vW%*FC$\"3`etArn+,=Fby7$$\"3S\"fk `m1Vd*FC$\"3/jN](*)3\"\\BFby7$$\"3$z+D\"G$eQq*FC$\"3q=+T)=inP$Fby7$$\" 3XCa)3**4M$)*FC$\"3K*\\d<%4w-gFby7$$\"33Uek`;'H'**FC$\"3%o/cTb/**p#!#: 7$$\"3(fiS;L^#45F6$!3QI(3)pa#43\"Ff[l7$$\"3inm\"z\\1A-\"F6$!3mK.dEk=.X Fby7$$\"3F4F>k;;N5F6$!3$fk;pX1S%GFby7$$\"3#4vo/$o6[5F6$!37ozdy[Fy?Fby7 $$\"3e#zWn*>2h5F6$!3'eg]qm6uj\"Fby7$$\"3YM3-jr-u5F6$!3ep+t&\\b3N\"Fby7 $$\"3KwoHHB)p3\"F6$!3w*f8jze'\\6Fby7$$\"3)z\"Hd&\\P**4\"F6$!3\"f]&>Nai +5Fby7$$\"3jf*[=m#*G6\"F6$!3q=tPm;(z&))F67$$\"3G,]7Gy%e7\"F6$!37!y3Eb/ h%zF67$$\"3%H/,W*H!)Q6F6$!3:dmsDbX/sF67$$\"3e%3x1;e<:\"F6$!3U2:Nr9V*e' F67$$\"3CEJ&pK8Z;\"F6$!3qSm:fT:rgF67$$\"35o\"HK\\ow<\"F6$!3ttdMe*f%GcF 67$$\"3k^7yD)yN?\"F6$!37>h&)4A57\\F67$$\"3%\\LL$e\"*[H7F6$!3Yc`4DV]dVF 67$$\"35o;/w\\-$G\"F6$!3^t*H&yqDLNF67$$\"3D,+v$zglL\"F6$!33drv/9BrHF67 $$\"3SM$e9h'4!R\"F6$!3qApfPvYjDF67$$\"3cnm;HCjV9F6$!3'\\*Qr^$=TD#F67$$ \"3)QL$ekSq]:F6$!3q;Cg2t&e\"=F67$$\"3=++++dxd;F6$!3j:0\\s]F?:F67$$\"3Q ++]7JFn=F6$!3%RND,KRI:\"F67$$\"3e+++D0xw?F6$!3m@NCV)HqG*FC7$$\"3%3+]P/ q%zAF6$!3n\"f@g$ft:yFC7$$\"35,+]i&p@[#F6$!3#3&4G'Qmou'FC7$$\"3++++vgHK HF6$!3'*)fY'\\.>v^FC7$$\"3ElmmmZvOLF6$!3?(z8h$FC7$$\"3UKL$eR<*fTF6$!3a3gZ(oRY;$FC7$$\"3K-++])Hxe%F6$! 3!f@uf'yF(y#FC7$$\"3!fmm\"H!o-*\\F6$!3j7u\\;t41DFC7$$\"3X,+]7k.6aF6$!3 ')\\@S44/nAFC7$$\"3#emmmT9C#eF6$!3Are^r+lt?FC7$$\"33****\\i!*3`iF6$!3[ (4:b\"=k.>FC7$$\"3;NLLL*zym'F6$!3'>0A$H\"GVw\"FC7$$\"3'eLL$3N1#4(F6$!3 Z#f$3L*z9k\"FC7$$\"3,pm;HYt7vF6$!3t`Wn=LXN:FC7$$\"37-+++xG**yF6$!3+v7> *)\\U\\9FC7$$\"3gpmmT6KU$)F6$!3][9!G7n>O\"FC7$$\"3qNLLLbdQ()F6$!3%*=$R ^[FAH\"FC7$$\"3[++]i`1h\"*F6$!3hA8.=-LD7FC7$$\"3A-+]P?Wl&*F6$!3GcE&*p? 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