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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 15e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 15e

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# Solved: Estimations with linear approximation Use linear

ISBN: 9780321570567 2

## Solution for problem 15E Chapter 4.5

Calculus: Early Transcendentals | 1st Edition

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Problem 15E

Estimations with linear approximation ?Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error. ?146

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Step 1 of 3

Solution 15E 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) = ;and choose a=144 We get f (x) = 1 2x 1 1 1 f(a) = 144 = 12and f (a) = 2 144= 2×12= 24 Therefore the Linear approximation of the function,f(x),near a point x=a, is L(x) = f(a)+f (a)(xa) 1 x 144 x x L(x) = 12+ (24144) = 12+ 24 24 = 12+ 24 6 = 6+ 24 L(x) = 6+ 24 STEP 3 According to the question 146 = f(146) f(146) L(146) = 6+ 146 = 12.083 24 Therefore 146 12.083

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Solved: Estimations with linear approximation Use linear