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Solution: Estimations with linear approximation Use linear

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

Solution for problem 17E 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 17E

Estimations with linear approximation ?Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error. ln(1.05)

Step-by-Step Solution:
Step 1 of 3

Solution 17E 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 (a)(xa) STEP 2 Here,let f(x) = ln(x) ;and choose a=1 1 We get f (x) = x f(a) = ln 1 = 0 and f(a) = = 1 1 Therefore the Linear approximation of the function,f(x),near a point x=a, is L(x) = f(a)+f (a)(xa) L(x) = 0+1(x1) = x1 L(x) = x1 STEP 3 According to the question ln(1.05) = f(1.05) f(1.05) L(1.05) = 1.051 = 0.05 Therefore ln(1.05) 0.05

Step 2 of 3

Chapter 4.5, Problem 17E 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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Solution: Estimations with linear approximation Use linear