of the maximum absolute error from parts( b)-( d). In particular, for parts( b) and( c), explain how your results are supported by what we saw in class regarding the bound of the maximum absolute error. Problem 2: Taylor‘ s polynomials for the sine function For this problem, you will approximate the sine function by its Taylor polynomials of increasing degree. The Taylor expansion for the sine function around x0 0 is sin x ¸8 p1qk x2k 1 x x3 p2k 1q! 3! k0 x5 5!
and it holds for all x P R. Your program will support this claim by plotting the Taylor polynomials ¸ p1qk x2k p2k 1q! k0 N 1 which approach the sine function as N increases. Write a Matlab function with the definition function [ c ] = sinPoly( n) where c is the vector of n Taylor polynomial is n). 1 coefficients of the Taylor polynomial of order n( i. e. the highest order of the Your function should check that the input variable n is odd. If it is even, it should print an error message and return c = 0. You may find the mod function useful here. Using your sinPoly function, plot on the same axes the function sinpxq and the Taylor polynomials of degree 5, 9, 13, 17, 21 in r2π, 2πs on a grid of 1000 equally spaced points. You may use polyval to evaluate the polynomials on the grid. Use a legend to label the plotted curves and