Consider the Maclaurin series: g(x)=sinx= x x³ x³ x² x⁹ x20+1 -...+ Σ(-1)º. 3! 5! 7! 91 n=0 (2n+1)! Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at x = (10 points) 6 Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x = 3π 2 to approximate g(4.8). Explain why your answer is so close to 1. (10 points) 263 x2n+1 Part C: The series: Σ (-1)"; has a partial sum S5 = (2n+1)! when x = 1. What is an interval, IS - S51 ≤ IR5| for which the actual sum exists? Provide an exact answer and justify your conclusion. (10 points) n=0 315