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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 9e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 9e

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# Answer: Linear approximation a. Write The equation of the

ISBN: 9780321570567 2

## Solution for problem 9E Chapter 4.5

Calculus: Early Transcendentals | 1st Edition

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Problem 9E

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 approxim?ation 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)? = ln(1 + ?x); ?a =0; ?f(0.9)

Step-by-Step Solution:
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Solution 9E STEP 1 Given f(x) = ln(1 + x);a = 0;f(0.9) 1 f x) = 1+x (a). Equation of the line of linear approximation y = L(x) = f(a) + f (a)(x ) Thus f(a) = ln (1 + 0) = ln 1 = 0 f (a) = 1 = 1 1+0 Therefore y = L(x) = f(a) + f (a)x a) y = 0 + 1(x 0) = x Thus we get y = x 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(0.9) L(0.9) 0.9 Therefore f(0.9) 0.9 STEP 4 (d). |approximate exact| Compute the percent error in your approximation: 100 × |exact| We get the exact value ,f(0.9)= ln(1 + 0.9) = 0.641 0.90.641 Then percent error = 100 × | |0.641|| = 40%

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