PK ])RBH mimetypetext/x-wxmathmlPK ])RQdBV5 5
format.txt
This file contains a wxMaxima session in the .wxmx format.
.wxmx files are .xml-based files contained in a .zip container like .odt
or .docx files. After changing their name to end in .zip the .xml and
eventual bitmap files inside them can be extracted using any .zip file
viewer.
The reason why part of a .wxmx file still might still seem to make sense in a
ordinary text viewer is that the text portion of .wxmx by default
isn't compressed: The text is typically small and compressing it would
mean that changing a single character would (with a high probability) change
big parts of the whole contents of the compressed .zip archive.
Even if version control tools like git and svn that remember all changes
that were ever made to a file can handle binary files compression would
make the changed part of the file bigger and therefore seriously reduce
the efficiency of version control
wxMaxima can be downloaded from https://github.com/wxMaxima-developers/wxmaxima.
It also is part of the windows installer for maxima
(https://wxmaxima-developers.github.io/wxmaxima/).
If a .wxmx file is broken but the content.xml portion of the file can still be
viewed using an text editor just save the xml's text as "content.xml"
and try to open it using a recent version of wxMaxima.
If it is valid XML (the XML header is intact, all opened tags are closed again,
the text is saved with the text encoding "UTF8 without BOM" and the few
special characters XML requires this for are properly escaped)
chances are high that wxMaxima will be able to recover all code and text
from the XML file.
PK ])R>@P @P content.xml
G1953 - Recuperación Examen Parcial 215 Enero 2021kill(all);f(x):=log(1+x);Obtener la expresión de la derivada n-esima de f(x)Se calculan las derivadas sucesivas, por ejemplo hasta orden 5makelist(diff(f(x),x,n),n,1,5);fn(x,n):=(-1)^(n-1)*((n-1)!/(x+1)^n);Obtener el polinomio de McLaurin de grado 5mcl5:taylor(f(x),x,0,5);wxplot2d([f(x),mcl5], [x,-3,4], [y,-5,3],[same_xy], [legend,"f(x)","MacLaurin-grado 5"]);Obtener la expresión general de la serie obtenida:a(n):=(-1)^(n-1)*x^n/n;En el caso concreto de la suma parcial 5-ésima que aproximaría el valor de f(x) en el entorno del origen (es decir, el polinomio calculado en el apartado 1.2):sum(a(n),n,1,5);kill(all);f(x):=atan(sin(x)/(1+cos(x)));define(f1(x),diff(f(x),x));La expresión de la derivada probablemente no resulta muy familiar en un principio, pero enseguida se reconoce aplicando simplificación de la expresión racional obtenida:ratsimp(f1(x));Aplicando una simplificación trigonométrica, llegamos al resultado final:trigsimp(f1(x));Al ser la derivada constante, se deduce que la gráfica de la función es una recta. Si representamos la función:wxplot2d(f(x),[x,-2*%pi,2*%pi], [same_xy]);La función f(x) es una función periódica (T=2π), siendo inyectiva si se considera el dominio (-π,π). Su dominio es R - {π+2kπ, k∈Z}. Vemos que efectivamente se trata de una recta, siendo por lo tanto su pendiente = 1/2 en cualquier punto de su dominio. Ecuación de la recta tangente en a=0:a:0;y-f(a)=f1(a)*(x-a);Ecuación de la recta secante en a=0:y-f(a)=(-1/f1(a))*(x-a);A continuación se representa gráficamente la función y la recta normal en el punto x=0. No se representa la recta tangente en x=0, ya que esta coincide con la propia función en el intervalo (-π,π):load(draw);wxdraw2d(proportional_axes=xy, grid=true, key="f(x)", explicit(f(x),x,-1.5*%pi,+1.5*%pi), color=red, key="recta normal", explicit(-2*x,x,-1,1), key="", point_type=filled_circle, point_size=2, color=red, points([[0,f(0)]]));kill(all);f(x):=exp(a)*exp(tan(x))/(4*(cos(x))^2);integrate(f(x),x);g(x):=(1/(3*b))*4^(sin(x^3))*cos(x^3)*3*x^2;integrate(g(x),x);h(x):=3*sin(2*x)/(5*sin(x)^2);integrate(h(x),x);I(x):=(2*x+5)/(x^2+2*x+5);integrate(I(x),x);kill(all);En un primer paso definimos la función a trozos mediante la estructura de control if-then-else:f(x,a):= if(x<0) then (1+a)*x/(1-x) else if(x>=0) then 2*x/(1+a*x);Tras el análisis descrito en la solución del ejercicio, se comprueba que la función sólo es derivable en (-1,1/2) para a=1.a:1;fxs:makelist(f(x,a),a,[-1,0,1,5]);wxplot2d([fxs[1],fxs[2],fxs[3],fxs[4]], [x,-1,1/2], [y,-1,1], [same_xy], [gnuplot_preamble, "set key top left"], [legend, "a=-1","a=0","a=1","a=5"], [title, "Gráfica de f(x) para diferentes valores de a"]);derivada_c : (f(1/2,a)-f(-1,a))/(1/2 - -1);Buscamos los valores de c que verifican el teorema:f_izquierda:(1+a)*x/(1-x);solve(diff(f_izquierda,x)=(9/10),x);f_derecha:2*x/(1+a*x);solve(diff(f_derecha,x)=(9/10),x);PK ])R<~8D 8D
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