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Cell["\<\
TAREA 2\.aa: DEFINICI\[CapitalOAcute]N Y REPRESENTACI\[CapitalOAcute]N DE \
FUNCIONES\
\>", "Title",
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Cell[TextData[{
 "Ejercicio 1:\nDada la fracci\[OAcute]n : (",
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 "), se pide:\n\ta) Descomponer en factores el numerador y denominador.\n\tb) \
Simplificarla.\n\tc) Descomponerla en fracciones parciales.\nRepetir estas \
operaciones utilizando la paleta\tALGEBRAICMANIPULATIONS. Para ello se marca \
la expresi\[OAcute]n correspondiente y se pincha en el comando de la paleta \
que se desee."
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Cell["\<\
En este ejercicio se utilizan los comandos de Mathematica Numerator, \
Denominator, Factor, Cancel, Simplify y Apart\
\>", "Text",
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Cell[TextData[{
 "Ejercicio 2\nDefinir f(x,y)= ",
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 ". Calcular f(1,0),  f(a+b, a-b) . \n"
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Cell["\<\
Ejercicio 3
Definir la funci\[OAcute]n vectorial de dos variables:
\t h(x,y) = { xcosy, ysinx) }.
Calcular h(1,0), h(\[Pi]/2, \[Pi]/2) y h(a+b, a-b).\
\>", "Subsection",
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Cell["\<\
Ejercicio 4
Representar las funciones senx, sen(2x) y sen(3x) conjuntamente en el \
intervalo [0, \[Pi]].\
\>", "Subsection",
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Cell[TextData[{
 "Ejercicio 5\nRepresentar, en primer lugar por separado y desp\[UAcute]es en \
un \[UAcute]nico gr\[AAcute]fico, \n\t- la hoja de Descartes ",
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 "\n\t- la cicloide ",
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 "\n"
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Cell["\<\
Como se trata de curvas dadas en forma param\[EAcute]trica, crearemos dos gr\
\[AAcute]ficos utilizando el comando ParametricPlot y despu\[EAcute]s los \
combinaremos con el comando GraphicsRow.\
\>", "Text",
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Cell[TextData[{
 "Ejercicio 6\nRepresentar la superfice de ecuaci\[OAcute]n z= ",
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Cell[TextData[{
 "Ejercicio 7\nRepresentar la superficie cuya ecuaci\[OAcute]n es:\nz=",
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Cell["\<\
Ejercicio 8
Representar la superficie cuya ecuaci\[OAcute]n es: z = cosy \[Times]sinx, en \
la regi\[OAcute]n:
\t\tx \[Element] [-\[Pi], \[Pi]], y \[Element] [-\[Pi], \[Pi]].
Generar cuatro gr\[AAcute]ficos distintos. 
- El primero, p1, utilizando la opci\[OAcute]n por defecto del comando Plot3D,
- El segundo, p2, utilizando la opci\[OAcute]n ColorFunction \[Rule] (White &),
- El tercero, p3, en verde con la opci\[OAcute]n ColorFunction \[Rule] \
(RGBColor[0,10, 0] /.\[InvisibleSpace]{x \[Rule] #1, y \[Rule] #2} &), y 
- El cuarto, p4,  con varias gamas de azul utilizando la opci\[OAcute]n \
ColorFunction \[Rule] (RGBColor[0,0,Abs[Cos[y]Sin[x] ]] /.\[InvisibleSpace]{x \
\[Rule] #1, y \[Rule] #2} &).\
\>", "Subsection",
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Cell[TextData[{
 "Ejercicio 9\nUtilizar el comando ParametricPlot para representar la \
circunferencia:\n",
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 " - 4x + ",
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  SuperscriptBox["y", "2"]]],
 "- 2y = 4."
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Cell[TextData[{
 "La ecuaci\[OAcute]n de una circunferencia de centro el punto (a, b) y de \
radio R viene dada por :\n\t",
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       RowBox[{"y", "-", "b"}], ")"}], "2"], "-", 
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 ".\nLa ecuaci\[OAcute]n dada es : ",
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 ", vamos a calcular a, b y R identificando los coeficientes de estos dos \
polinomios de segundo grado. Para ello utilizaremos el comando Coefficient de \
",
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 " que podemos explorar previamente en la Ayuda.\n\t"
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Cell[TextData[{
 "Ejercicio 10\nRepresentar de varias formas distintas la circunferencia  : ",
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Cell["\<\
La forma mas sencilla de representar la circunferencia dada es utilizando el \
comando ContourPlot. Utilizamos opciones del comando como las que representan \
los ejes y eliminan el marco. Ademas con la opci\[OAcute]n ContourStyle \
representamos la circunferencia en trazo grueso y rojo.\
\>", "Text",
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Cell["\<\
Para representar la circunferencia mediante el comando ParametricPlot hacemos \
lo mismo que en el ejercicio anterior para calcular el centro y el radio. En \
este caso, vamos a simplificar el c\[AAcute]lculo calculando unicamente el \
radio. \
\>", "Text",
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Cell["\<\
Finalmente vamos a representar cada una de las ramas de la circunferencia \
despejando y en la ecuaci\[OAcute]n impl\[IAcute]cita y utilizando el comando \
Plot para generar dos gr\[AAcute]ficos que luego se muestran conjuntamente \
con el comando Show.\
\>", "Text",
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Cell[TextData[{
 "Ejercicio 11\nSea f(x) = ",
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 "+2x+2 y g(x) = x+1. Obtener las siguientes composicones de funciones:\n\t- \
f",
 Cell[BoxData[
  FormBox["\[SmallCircle]", TraditionalForm]]],
 "f(x)\n\t- f",
 Cell[BoxData[
  FormBox["\[SmallCircle]", TraditionalForm]]],
 "g(x)\n\t- g",
 Cell[BoxData[
  FormBox["\[SmallCircle]", TraditionalForm]]],
 "f(x)\n\t- g",
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 "g(x)\n"
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