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(a) Find the Taylor polynomials up to degree 5 for f(x) - sin(x) centered at a - 0. To(x) = T;(x) = T,(x) T3(x) = Ta(x) = T5(x)

(a) Find the Taylor polynomials up to degree 5 for f(x) - sin(x) centered at a - 0. To(x) = T;(x) = T,(x) T3(x) = Ta(x) = T5(x)

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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(a) Find the Taylor polynomials up to degree 5 for f(x) = sin(x) centered at a = 0. To(x) = T,(x) = T3(x) : T4(x) = T5(x) = Graph f and these polynomials on a common screen. AA 1.0 \1.0 1.0 0.5 05 0.5 -6 -4 -2 2 4 6. -4 -2 2 4 6 -6 -4 4 6 0.5 -0.5 -0.5 1.0 -1.0F -1.0
Transcribed Image Text:(a) Find the Taylor polynomials up to degree 5 for f(x) = sin(x) centered at a = 0. To(x) = T,(x) = T3(x) : T4(x) = T5(x) = Graph f and these polynomials on a common screen. AA 1.0 \1.0 1.0 0.5 05 0.5 -6 -4 -2 2 4 6. -4 -2 2 4 6 -6 -4 4 6 0.5 -0.5 -0.5 1.0 -1.0F -1.0
1.0 0.5 -6 -4 -2 4 -0/5 71.0 (b) Evaluate f and these polynomials at x = and n. (Round your answers to four decimal places.) 4' 2 To I1 = T2 T3 = T4 T5 (c) Comment on how the Taylor polynomials converge to f(x). As n increases, T,(x) is a good approximation to f(x) on a Select--- v interval.
Transcribed Image Text:1.0 0.5 -6 -4 -2 4 -0/5 71.0 (b) Evaluate f and these polynomials at x = and n. (Round your answers to four decimal places.) 4' 2 To I1 = T2 T3 = T4 T5 (c) Comment on how the Taylor polynomials converge to f(x). As n increases, T,(x) is a good approximation to f(x) on a Select--- v interval.
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