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How is the remainder in a Taylor polynomial defined?

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

Solution for problem 5E Chapter 9.1

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 5E

Problem 5E

How is the remainder in a Taylor polynomial defined?

Step-by-Step Solution:

Solution 5E

Step 1:

Remainder in a taylor polynomial() ;Suppose that f is n+1 times differentiable and let  denote the difference between f(x) and the Taylor polynomial of degree n for f(x) centered at a.

                       Then,  (x) = f(x) - (x) = .

  That is ,

                                       

  Taylor series; f(a) +++............

Taylor polynomial ; f(a) ++

Remainder term ;(x) = ++………….

                          | (x)| = |  |.

Step 2 of 1

Chapter 9.1, Problem 5E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Since the solution to 5E from 9.1 chapter was answered, more than 257 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 5E from chapter: 9.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “How is the remainder in a Taylor polynomial defined?” is broken down into a number of easy to follow steps, and 9 words. This full solution covers the following key subjects: defined, polynomial, Remainder, Taylor. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

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How is the remainder in a Taylor polynomial defined?