Consider the Maclaurin series: g(x)=sinx = x- X20+1 31 51 71 91 -1) (2n+1)! Part A:...

Transcribed Image Text:

Consider the Maclaurin series: g(x)=sinx = x- X20+1 31 51 71 91 -1)" (2n+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) Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x= your answer is so close to 1. (10 points) to estimate g(1.6). Explain why 2 Part C: The series: (-1)"; x2n+1 has a partial sum S3 n=0 (2n+1)! 101 120 when x = 1. What is an interval, |S - S3| |R3| for which the actual sum exists? Provide an exact answer and justify your conclusion. (10 points) Format Toole Table Consider the Maclaurin series: g(x)=sinx = x- X20+1 31 51 71 91 -1)" (2n+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) Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x= your answer is so close to 1. (10 points) to estimate g(1.6). Explain why 2 Part C: The series: (-1)"; x2n+1 has a partial sum S3 n=0 (2n+1)! 101 120 when x = 1. What is an interval, |S - S3| |R3| for which the actual sum exists? Provide an exact answer and justify your conclusion. (10 points) Format Toole Table