Using the proof of Theorem 7 58, prove that (20) holds if r 2 replaces r Use part a) to estimate the difference 4 , where x0 3, f(x) sin x, and xn is defined by (19) Evaluate x4 directly, and verify that x4 is actually closer than the theory predicts ...

Let a 3 b 4 and fx sin x Then fx cos x fx sin x Therefore ...

Using the proof of Theorem 7.58, prove that (20) holds if r/2 replaces r. Use part a)

Question:

Using the proof of Theorem 7.58, prove that (20) holds if r/2 replaces r.
Use part a) to estimate the difference |π4 - π|, where x0 = 3, f(x) = sin x, and xn is defined by (19). Evaluate x4 directly, and verify that x4 is actually closer than the theory predicts.