Consider the Maclaurin series: g(x) = sinx = x_ x x _x' x x 20-1 31 51 71 91 -...+ X-1 (2n +1)1 Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(2x) centered at x = . (10 points) 2 Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x = to estimate g(1.6) out to five decimal places. Explain why your answer is so close to 1. (10 points) Part C: The series: ) (_nn x20+1 has a partial sum S, = 13 (2n + 1)1 15 when x = 1. What is an interval, IS - Sal s |Ral for which the actual sum exists? Provide an exact answer and justify your conclusion. (10 points)