Math 112: MATLAB Assignment 2

Taylor Series and Polynomials

Due Date: APRIL 18, 2008

The sample program below calculates 2^nd and 4^th degree Taylor polynomials for the function f(x)=1/(1+x^2) about the point a=0. The polynomials are plotted, together with the function, over the interval x=-1, 1.

% Lines beginning with a percent sign (%) are comments

% construct Taylor polynomials.

clear;

x=[-1: .01:1];

y=(1+x.^2).^(-1);

P2=1-x.^2;

P4=1-x.^2+x.^4;

plot(x,y)

hold on

plot(x,P2,'--')

hold on

plot(x,P4,':')

grid on

After running the above example, do the following to hand in: (Consult the MATLAB TA's if you have any questions.)

◙  Calculate the 2^nd and 3^rd degree Taylor polynomials for the function y=ln(1+x) about the point a=0.

◙  Plot these polynomials and the function on the interval -1<x<3.