Consider the Maclaurin series: g(x)=sinx=x- X³ X5 X² X⁹ 31 51 7! 9! + Σ (−1)² x20+1 (2n+1)! (10 points) Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at x = 픔.. 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) 00 263 Part C: The series: Σ (-1)" x2n+1 has a partial sum S₁ (2n+1)! when x = 1. What is an interval, IS - S5 ≤ IR5l for which the actual sum exists? Provide an exact answer and justify your conclusion.
