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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 40e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 40e

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# Solution: Linear approximation Write an equation of the line

ISBN: 9780321570567 2

## Solution for problem 40E Chapter 4.5

Calculus: Early Transcendentals | 1st Edition

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Problem 40E

Linear approximation ?Write an equation of the line that represents the linear approximation To the following functions at a. Then (?a? ?graph the function and the linear approximation near a: (?? ?use the linear approximation to estimate the given quantity; and (?? ?compute the percent error in your approximation. f? ?) = tan? ?; ?a? =0; tan 1.5°

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Solution 40E STEP 1 .The linear approximation formula is given by y = L(x) = f(a)+f (a)(xa) Given f(x) = tan x and a = 0. f(a) = tan 0 = 0 Then f (x) = sec x f(a) = sec 0 = 1 Therefore y = L(x) = 0+1(x0) = x Thus we get L(x) = x Thus we get the equation of the line as y = x STEP 2 (a).graph the function and the linear approximation near a: STEP 3 (b). use the linear approximation to estimate the given quantity; o We have to estimate the value of tan 1.5 using the linear approximation Thus we have o tan 1.5 L(1.5) = 1.5 o Thus tan 1.5 = 1.5 STEP 4 (c) .compute the percent error in your approximation. o The exact value of tan 1.5 = 0.026 |approxexact| |1.50.026| Therefore percent error = 100× |exact| = 100× |0.026|= 100×56.467 = 5646.7% percent error = 5646.7%

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