1.99
See Answer

In Section 4.8 we considered Newton’s method for approximating a root r of the equation f(x) = 0, and from an initial approximation x1 we obtained successive approximations x2, x3, . . . , where

Use Taylor’s Inequality with n = 1, a = xn, and x = r to show that if f 0(x) exists on an interval I containing r, xn, and xn11, and /

f(xm) f'(x„) Xn+1 | S"(x)| < M, | f'(x)| > K for all x E I, then