Explanation Given: The function is f ( x ) = 1 x + 1 . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Calculation: The function is f ( x ) = 1 x + 1 . We need to estimate Δ f = f ( 3.02 ) − f ( 3 ) by using linear approximation of Δ f . Here, Δ f = f ( a + Δ x ) − f ( a ) . Differentiate the function with respect to x f ′ ( x ) = − 1 ( x + 1 ) 2 Now, apply the linear approximation with a = 3 and Δ x = 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.1, Problem 4E

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Estimate the value of Δf=f(3.02)−f(3) by using f(a+Δx)≈f(a)+f′(a)Δx.

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Chapter 4.1, Problem 3E

Chapter 4.1, Problem 5E

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Chapter 4 Solutions

Calculus - Standalone book

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Estimate the value of Δ f = f ( 3.02 ) − f ( 3 ) by using f ( a + Δ x ) ≈ f ( a ) + f ′ ( a ) Δ x .

Solution Summary: The author explains how to estimate the value of Delta f by using a linear approximation.

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Estimate the value of Δf=f(3.02)−f(3) by using f(a+Δx)≈f(a)+f′(a)Δx.

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Chapter 4 Solutions