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Solution: Linear approximation a. Write The equation of the

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

Solution for problem 10E 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 10E

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 • l approx-exact| / |exact| f?(?x?)? ?? ? + 1): ?a? = ? ?(1.1)

Step-by-Step Solution:
Step 1 of 3

Solution 10E STEP 1 x Given f(x) = 1+x;a = 1;f(1.1) f(x) = x = x(x + 1) 1 1+x By using the product rule,we get 1 f x) = (x+1)2 (a). Equation of the line of linear approximation y = L(x) = f(a) + f (a)(x a) 1 1 Thus f(a) = 1+1 = 2 f a) = 1 2 = 1 (1+1) 4 Therefore y = L(x) = f(a) + f (a)x a) 1 1 1 1 1 1 1 y = 2 + (4 1) = 2 + 4 4 = 4 + 4 Thus we get y = x + 1 = x+1 4 4 4 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(1.1) L(1.1) 1.1+1 4 = 0.525 Therefore f(1.1) 0.525 STEP 4 (d). |approximate exact| Compute the percent error in your approximation: 100 × |exact| 1.1 We get the exact value ,f(1.1)= 1+1.1 = 0.523 Then percent error = 100 × |.5250.523 |= 0.38% |0.523|

Step 2 of 3

Chapter 4.5, Problem 10E is Solved
Step 3 of 3

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

Since the solution to 10E from 4.5 chapter was answered, more than 282 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 10E from chapter: 4.5 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. 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 85 chapters, and 5218 solutions. 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 • l approx-exact| / |exact| f?(?x?)? ?? ? + 1): ?a? = ? ?(1.1)” is broken down into a number of easy to follow steps, and 71 words.

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Solution: Linear approximation a. Write The equation of the