Chapter 6, Problem 25P

The Taylor series expansion for a^xis:

$a^x={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{{(\ln a)}^n}{n!}{x}^n}$

Write a MATLAB program that determines a^xusing the Taylor series expansion. The program asks the user to type a value for x. Use a loop for adding the terms of the Taylor series. If c_nis the nth term in the series, then the sum S_nof the n terms is =S_n= S S_n-1+c_n. In each pass calculate the estimated error E given by $E=\left|\frac{S_n-S_{n-1}}{S_{n-1}}\right|$ . Stop adding terms when E<0.000001. The program displays the value of a^x. Use the program to calculate:

(a) 2³.5(b) 6.3¹.7

Compare the values with those obtained by using a calculator.