Question 1 (Essay Worth 30 points) (10.07 HC) x20+1 Consider the Maclaurin series: g(x) = sinx = x- x x x x x 3! 51 7! 9! -...+ (-1)- (2n + 1)! Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at x = 4. (10 points) 2 Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x =>" to approximate g(4.8). Explain why your answer is so close to -1. (10 points) Part C: The series: I (-10 x20+1 (2n + 1)! has a partial sum S5 = 305353 when x = 1. What is an interval, IS - Ss] s |Rs) for which the actual sum exists? Provide an exact answer and justify your 1=0 362880 conclusion. (10 points)