(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 31966, 789] NotebookOptionsPosition[ 14353, 454] NotebookOutlinePosition[ 30995, 754] CellTagsIndexPosition[ 30952, 751] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ TAREA 3\.aa: Introducci\[OAcute]n a las listas y tablas\ \>", "Title", CellChangeTimes->{3.427778666641778*^9}], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 1\nGenerar de varias formas distintas la lista:", Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", FractionBox["3", "2"], ",", "2", ",", FractionBox["5", "2"], ",", "3", ",", FractionBox["7", "2"], ",", "4"}], "}"}]]], ", asign\[AAcute]ndole el nombre: listauno." }], "Subsection", TextAlignment->Left, TextJustification->1], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.472217918734375*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ejercicio 2 Crear una lista con los 25 primeros n\[UAcute]meros primos utilizando el \ comando Prime. \[DownQuestion]Cu\[AAcute]l es el decimoquinto n\[UAcute]mero \ primo?\ \>", "Subsection", TextAlignment->Left, TextJustification->1], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.472217924765625*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ejercicio 3 a) Generar una lista formada por cinco copias de la letra a. b) Generar una lista formada por 10 enteros aleatorios entre -10 y 10. \ (Utilizar el comando RandomInteger)\ \>", "Subsection", CellChangeTimes->{{3.4277786943638563`*^9, 3.4277787105719757`*^9}}, TextAlignment->Left, TextJustification->1], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.47221792871875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 4\nCalcular una aproximaci\[OAcute]n del n\[UAcute]mero \[Pi] de \ 101 d\[IAcute]gitos y crear una lista de nombre ", StyleBox["digitos", FontVariations->{"Underline"->True}], " que los contenga (Utilizar el comando RealDigits). \[DownQuestion]Cu\ \[AAcute]ntas veces aparece cada d\[IAcute]gito en la aproximaci\[OAcute]n?\ \[DownQuestion]Qu\[EAcute] d\[IAcute]gito ocupa la posici\[OAcute]n 66 a la \ derecha de la coma decimal?(Utilizar el comando Count y TableForm)" }], "Subsection", TextAlignment->Left, TextJustification->1], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.472217936296875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 5\nLa siguiente tabla presenta el porcentaje de trabajadores que \ pertenec\[IAcute]an a alg\[UAcute]n sindicato en U.S.A. en el a\[NTilde]o \ indicado. Representar gr\[AAcute]ficamente los datos de la tabla.\n\ A\[NTilde]o % Trab.\n", Cell[BoxData[GridBox[{ {"1930", StyleBox["11.5999999999999992`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1935", StyleBox["13.1999999999999984`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1940", StyleBox["26.8999999999999994`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1945", StyleBox["35.4999999999999982`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1950", StyleBox["31.4999999999999991`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1955", StyleBox["33.2000000000000028`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1960", StyleBox["31.3999999999999968`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1965", StyleBox["28.3999999999999985`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1970", StyleBox["27.2999999999999998`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1975", StyleBox["25.4999999999999982`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1980", StyleBox["21.8999999999999994`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1985", StyleBox["18.`", StyleBoxAutoDelete->True, PrintPrecision->3]}, {"1990", StyleBox["16.1000000000000014`", StyleBoxAutoDelete->True, PrintPrecision->3]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[2.0999999999999996`]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}]]] }], "Subsection", TextAlignment->Left, TextJustification->1], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.472217941953125*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ejercicio 6 Obtener una tabla con los valores de las funciones trigonom\[EAcute]tricas: \ sen, cos y tg de los \[AAcute]ngulos principales \ \>", "Subsection", TextAlignment->Left, TextJustification->1], Cell["\<\ En primer lugar se construye la lista de los \[AAcute]ngulos principales, \ tomando de 0 a 2\[Pi] con incrementos de \[Pi]/4, y de 0 a 2\[Pi] con \ incrementos de \[Pi]/6.\ \>", "Text", TextAlignment->Left, TextJustification->1], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.47221796346875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 7\nSea f(x) = ", Cell[BoxData[ RowBox[{ SuperscriptBox["x", "3"], "-", FractionBox[ RowBox[{"9", SuperscriptBox["x", "2"]}], "2"], "+", FractionBox[ RowBox[{"23", "x"}], "4"], "-", FractionBox["15", "8"]}]]], ".\nRepresentar f y la linea tangente que pasa por el punto (a,f(a)) y el \ punto, para distintos valores de a. Realizar el ejercicio siguiendo los \ pasos,\n1\.ba.- Almacenar en una variable graff la representaci\[OAcute]n gr\ \[AAcute]fica de f en el intervalo [0 , 4].\n2\.ba.- Definir una funci\ \[OAcute]n que de la tangente que pasa por los puntos (a,f(a)) .\n3\.ba.- \ Obtener la tangente correspondiente a a=1 .\n4\.ba.- Crear una lista, tans, \ que contenga las gr\[AAcute]ficas de las tangentes que pasan por los punto \ (1+h, f(1+h)), con h variando de 0 a 3 y de 0.5 en 0.5.\n5\.ba.- Crear otra \ lista, punto, con la representaci\[OAcute]n gr\[AAcute]fica de los puntos de \ la curva en los que se traza la tangente. Utilizar los comandos Graphics y \ Point, con un tama\[NTilde]o dado por la opci\[OAcute]n PointSize[0.02].\n6\ \.ba.- Crear otra lista gr\[AAcute]ficas en las que se represente la funci\ \[OAcute]n, cada una de las tangentes y el punto de tangencia.\n7\.ba.- \ Finalmente utilizar el comando Animate para hacer una animaci\[OAcute]n de \ las gr\[AAcute]ficas obtenidas." }], "Subsection", CellChangeTimes->{{3.427603541517315*^9, 3.427603625856372*^9}, { 3.427603684537407*^9, 3.427603688565506*^9}, {3.427603864956152*^9, 3.42760396948619*^9}, {3.427604005052812*^9, 3.4276040631847887`*^9}}, TextAlignment->Left, TextJustification->1], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.47221797303125*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ejemplo 8 La tabla siguiente muestra el porcentaje de productos derivados del petroleo \ importado por U.S.a. en ciertos a\[NTilde]os. a) Representar gr\[AAcute]ficamente los puntos correspondientes uniendo \ puntos consecutivos mediante segmentos. b) Utilizar el comando InterpolatingPolynomial para hallar una \ funci\[OAcute]n que aproxime los datos de la tabla. c) Hallar el polinomio de aproximaci\[OAcute]n de grado cuatro. d) Hallar una aproximaci\[OAcute]n trigonom\[EAcute]trica tomando como \ funciones base: 1, sin(x), sin(x/2), cos(x) y cos(x/2).\ \>", "Subsection", CellChangeTimes->{{3.427805857643763*^9, 3.427805869643278*^9}, { 3.427805914318798*^9, 3.427805956894622*^9}}, TextAlignment->Left, TextJustification->1], Cell[BoxData[ FormBox[ TagBox[GridBox[{ { StyleBox["1973.00000000000004`", StyleBoxAutoDelete->True, PrintPrecision->4], StyleBox["34.8104999999999975`", StyleBoxAutoDelete->True, PrintPrecision->6]}, { StyleBox["1974.00000000000019`", StyleBoxAutoDelete->True, PrintPrecision->4], StyleBox["35.3810000000000002`", StyleBoxAutoDelete->True, PrintPrecision->5]}, { StyleBox["1975.`", StyleBoxAutoDelete->True, PrintPrecision->4], StyleBox["35.816699999999999`", StyleBoxAutoDelete->True, 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