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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) %3D Graph fand these polynomials on a common screen.

(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) %3D Graph fand these polynomials on a common screen.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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) T2(x) = || T3(x) = T4(x) = T5(x) = Graph f and these polynomials on a common screen. AA A VA 1.0 1.0 1.0 0.5 0.5 0.5 -6 -4 -2 4 -4 |-2 4 6 -6 -4 4 6 0.5 -0.5 -0.5 1.0 -1.0 -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) T2(x) = || T3(x) = T4(x) = T5(x) = Graph f and these polynomials on a common screen. AA A VA 1.0 1.0 1.0 0.5 0.5 0.5 -6 -4 -2 4 -4 |-2 4 6 -6 -4 4 6 0.5 -0.5 -0.5 1.0 -1.0 -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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