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Errors in approximations Suppose f(x) = 1/(1 + x) is to be

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

Solution for problem 46E Chapter 4.5

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 46E

Errors in approximations Suppose ?f?(?x?) = 1/(1 + ?x?) is to be approximated near x? = 0. Find the linear approximation ?t? of a? ? = 0. Then, complete the following table showing the errors in various approximations. Use a calculator to obtain the exact values. The percent error is 100 • | approximation - exact | / | exact |. Comment on the behavior of the errors as ?x approaches 0.

Step-by-Step Solution:
Step 1 of 3

SOLUTION STEP 1 .The linear approximation formula is given by L(x) = f(a) + f(a)(x a) Given f(x) = 1+x and a = 0. f(a) = 1 = 1 1+0 1 1 Then f x) = (1+x) f(a) = 1 = 1 Therefore L(x) = 1 1(x 0) = 1 x Thus we get L(x) = 1 x x Linear Exact Percent approx value error 0.1 0.9 0.9090 0.99009 9 9 0.01...

Step 2 of 3

Chapter 4.5, Problem 46E is Solved
Step 3 of 3

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

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Errors in approximations Suppose ?f?(?x?) = 1/(1 + ?x?) is to be approximated near x? = 0. Find the linear approximation ?t? of a? ? = 0. Then, complete the following table showing the errors in various approximations. Use a calculator to obtain the exact values. The percent error is 100 • | approximation - exact | / | exact |. Comment on the behavior of the errors as ?x approaches 0.” is broken down into a number of easy to follow steps, and 72 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: exact, errors, Approximation, approximations, approaches. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 46E from chapter: 4.5 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 46E from 4.5 chapter was answered, more than 278 students have viewed the full step-by-step answer.

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