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Best expansion point Suppose you wish to approximate e0.35

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

Solution for problem 83E 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 83E

Problem 83E

Best expansion point Suppose you wish to approximate e0.35 using Taylor polynomials. Is the approximation more accurate if you use Taylor polynomials centered at 0 or In 2? Use a calculator for numerical experiments and check for consistency with Theorem 9.2. Does the answer depend on the order of the polynomial?

Step-by-Step Solution:

Solution 83E

Step 1:

Given function is f(x) =

             

 General  expression of Taylor series of  a function f(x) centered at ‘a’ is ;

          f(a) +(x-a) +++.............

 Consider , f(x) =  , then f(0) =  = 1

                 =  , then     = = 1

                    =  , then     =  = 1

                      =  , then     =  = 1

  =  , then     =  = 1 ……………..

Therefore , the Taylor polynomial  of the function f(x) = with center zero is ;

                  = 1+x +++.............

Take  x= 0.35 , then we get ,

           = 1+ 0.35 +++.............

                          1+0.35 +0.06125+0.007145833+...........

                           1.4183958333

Step 2 of 3

Chapter 9.1, Problem 83E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The answer to “Best expansion point Suppose you wish to approximate e0.35 using Taylor polynomials. Is the approximation more accurate if you use Taylor polynomials centered at 0 or In 2? Use a calculator for numerical experiments and check for consistency with Theorem 9.2. Does the answer depend on the order of the polynomial?” is broken down into a number of easy to follow steps, and 51 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: polynomials, use, Taylor, Experiments, Best. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 83E from chapter: 9.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 83E from 9.1 chapter was answered, more than 329 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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Best expansion point Suppose you wish to approximate e0.35