v u m ,- . . . a x' x' x x ' . x' ConSIder the Maclaurln series: x - smx x e - w m ; - - 1 ' f g( ) 3! 5! 7! 9! Z( } (2n 9- 1)! Part A: Find the coefcient of the 4th degree term in the Taylor polynomial for f(x) = sin(3x) centered at x : g (10 points) Part B: Use a 4th degree Taylor polynomial for cos(x) centered at x : 11' to estimate g(3.'|). Explain why your answer is so close to -'l. (10 points) no 2n+1 Part C: The series: E (4)\" x has a partial sum 3 2 13 when x =1. What is an interval, IS - S4| s |R4| for n ,0 (2n+1).' " 105 which the actual sum exists? Provide an exact answer and justify your conclusion. (1 0 points)