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X³ X5 X7 Consider the Maclaurin series: g(x)=sinx= x -+ 31 51 71 9! x⁹ x2n+1 (2n+1)! Зл Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x => why your answer is so close to 1. Part C: The series: (-1)" - has a partial sum S₁ = ... + +Σ(-1)º n=0 305353 362880 x20+1 (2n+1)! to approximate g(4.8). Explain when x = 1. What is an interval, IS - S5l n=0 ≤ R5 for which the actual sum exists? Provide an exact answer and justify your conclusion.

X³ X5 X7 Consider the Maclaurin series: g(x)=sinx= x -+ 31 51 71 9! x⁹ x2n+1 (2n+1)! Зл Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x => why your answer is so close to 1. Part C: The series: (-1)" - has a partial sum S₁ = ... + +Σ(-1)º n=0 305353 362880 x20+1 (2n+1)! to approximate g(4.8). Explain when x = 1. What is an interval, IS - S5l n=0 ≤ R5 for which the actual sum exists? Provide an exact answer and justify your conclusion.

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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Solve Part B and Part C on paper

Consider the Maclaurin series: g(x)=sinx= x- + 3! 5! + 7! 9! www + Σ(-1)^ Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x = why your answer is so close to 1. 305353 362880 n=0 20+1 (2n + 1)! Зл 37 to approximate g(4.8). Explain 2 x2n+1 Part C: The series: Σ (-1)"; has a partial sum S₁ (2n+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- + 3! 5! + 7! 9! www + Σ(-1)^ Part B: Use a 4th degree Taylor polynomial for sin(x) centered at x = why your answer is so close to 1. 305353 362880 n=0 20+1 (2n + 1)! Зл 37 to approximate g(4.8). Explain 2 x2n+1 Part C: The series: Σ (-1)"; has a partial sum S₁ (2n+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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