In: Advanced Math
a) For the function f (x) = x – exp(−x2), do a calculation by hand using a calculator to find the root to an accuracy of 0.1. At most, five iterations (or fewer) are needed to obtain the desired accuracy.
b) For f (x) = x2 – sin x, x0 = 1⁄2, do three iterations of Newton’s method (by hand); tabulate the result.