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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 8e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 8e

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# Solved: Linear approximation a. Write The equation of the ISBN: 9780321570567 2

## Solution for problem 8E Chapter 4.5

Calculus: Early Transcendentals | 1st Edition

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Problem 8E

Linear approximation a. Write The equation of the line that represents the linear approximation to the following functions at the given point a. b. Graph the function and the linear approximation near x? = a ? . c. Use the linear approximation to estimate the given function value. d. Compute the percent error in your approximation:? 100 • lapprox-exact| / |exact| f?(?x?)=sin ?x?: ?a? = ?/4; ?f?(0.75)

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Solution 8E SOLUTION STEP 1 Given f(x) = sin x;a = /4;f(0.75) f x) = cos x (a). Equation of the line of linear approximation y = L(x) = f(a) + f (a)(x a) Thus f(a) = sin /4 = 1 2 1 f a) = cos /4 = 2 Therefore y = L(x) = f(a) + f (a(x a) y = 1 + 1 (x 4 = 1 (x 4 + 1) 2 2 2 1 Thus we get y = 2(x 4 + 1) STEP 2 (b).Graph the function and the linear approximation near x = a. STEP 3 (c). Use the linear approximation to estimate the given function value. We have f(0.75) L(0.75) 1 2(0.75 4+ 1) 0.682 Therefore f(0.75) 0.682 STEP 4 (d). |approximate exact| Compute the percent error in your approximation: 100 × |exact| We get the exact value ,f(0.75)= sin(0.75) = 0.681 0.6820.681 Then percent error = 100 × | |0.681| | = 0.14%

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##### ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 8E from 4.5 chapter was answered, more than 471 students have viewed the full step-by-step answer. The answer to “Linear approximation a. Write The equation of the line that represents the linear approximation to the following functions at the given point a. b. Graph the function and the linear approximation near x? = a ? . c. Use the linear approximation to estimate the given function value. d. Compute the percent error in your approximation:? 100 • lapprox-exact| / |exact| f?(?x?)=sin ?x?: ?a? = ?/4; ?f?(0.75)” is broken down into a number of easy to follow steps, and 67 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: Approximation, Linear, given, function, exact. This expansive textbook survival guide covers 112 chapters, and 5248 solutions. The full step-by-step solution to problem: 8E from chapter: 4.5 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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