Problem 1. The Maclaurin series of sin(x) is ) (-1)" (2n + 1)! (see Key Idea 8.8.1). n=0 (a) (3 points) Show that this is indeed the Maclaurin series of sin(r). (b) (4 points) Estimate sin(-0.1) using the Taylor polynomial of degree 3 centered at (). What is the maximum possible error of this estimation? (c) (4 points) Show that sin(r) is analytic. (d) (4 points) Find n such that the nth degree Taylor polynomial of sin(c) centered at 0 approximates sin(2.5) to within 0.0001 of the actual answer. (Hint: See Example 8.7.4 in the textbook)