Test your program for x 10 2 -2 and -10 from the plots

Question

Consider the Taylor expansion for the exponential

e^x = 1 + x + x²/2! + x³/3! +...... = lim_N→∞ S(x, N)

where S(x, N) is the partial sum with N +1 terms. (a) Write a program that plots the absolute fractional error of the sum, |S(x,N)- e^x |e^x, versus N (up to N = 60) for a given value of x. Test your program for x = 10, 2, -2, and -10. From the plots, explain why this is not a good way to evaluate 9 when x < 0449] (b) Modify your program so that it uses the identity e^x =1/e-^x = 1/S (-x, ∞) to evaluate the exponential when x is negative. Explain why this approach works better.