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Consider the Maclaurin series: g(x)=sinx= x- + 31 51 71 91 X= 20+1 (2n+1)! + Σ(-1)"; A=0 Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at T 6

Consider the Maclaurin series: g(x)=sinx= x- + 31 51 71 91 X= 20+1 (2n+1)! + Σ(-1)"; A=0 Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at T 6

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the Maclaurin series: g(x) = sinx= x- X = x³ x5 X² x⁹ + + 3! 51 7! 9! x²n+1 (2n+1)! Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at 元 6 has a partial sum S₁ = = x20+1 (2n + 1)! + +Σ(-1)²- n=0 3A 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. 305353 362880 Part C: The series: Σ (-1)"; n=0 ≤ R5| for which the actual sum exists? Provide an exact answer and justify your conclusion. when x = 1. What is an interval, IS - S51
Transcribed Image Text:Consider the Maclaurin series: g(x) = sinx= x- X = x³ x5 X² x⁹ + + 3! 51 7! 9! x²n+1 (2n+1)! Part A: Find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at 元 6 has a partial sum S₁ = = x20+1 (2n + 1)! + +Σ(-1)²- n=0 3A 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. 305353 362880 Part C: The series: Σ (-1)"; n=0 ≤ R5| for which the actual sum exists? Provide an exact answer and justify your conclusion. when x = 1. What is an interval, IS - S51
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