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

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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...

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Answer: Linear approximation a. Write The equation of the

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