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Estimations with linear approximation Use | Ch 4.5 - 21E

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

Solution for problem 21E 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 21E

Estimations with linear approximation ?Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error. 1 ?510

Step-by-Step Solution:
Step 1 of 3

Solution 21E STEP 1 Linear approximation is a method of estimating the value of a function,f(x),near a point x=a,using the formula L(x) = f(a) + f ()(x a) STEP 2 3 Here,let f(x) = 1/ x;and choose a=512 We get f () = 14 3x3 f(a) = 3 1 = 8 and f(a) = 1 4 = 3×4096 = 12288 512 3(512)3 Therefore the Linear approximation of the function,f(x),near a point x=a, is L(x) = f(a) + f (a)(x a) L(x) = 8 12288 (x 512) STEP 3 1 According to the question 3 = f(510) 510 f(510) L(510) = 8 12288(510 512) = 0.1252 1 Therefore 510 0.1252

Step 2 of 3

Chapter 4.5, Problem 21E is Solved
Step 3 of 3

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

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Estimations with linear approximation Use | Ch 4.5 - 21E