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In terms of the remainder, what does it mean for a Taylor

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 7E Chapter 9.3

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 7E

In terms of the remainder, what does it mean for a Taylor series for a function f to converge to f?

Step-by-Step Solution:

Solution 7EStep 1:In this problem we need to say, in terms of the remainder, what does it mean for a Taylor series for a function f to converge to fSuppose f is infinitely differentiable on an open interval I that contains a point c. Suppose for each x in I, there exists a real number such that for all n and y between c and x.Let for each x in I, the remainder term for order Taylor series is for some point b between c and x.By assumption we have for all n and y between c and x.This last sequence converges to 0 for each x. This means that the Taylor series of f converges to f itself.

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Chapter 9.3, Problem 7E is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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In terms of the remainder, what does it mean for a Taylor