Explanation Given information: f ( x ) = 1 x , a = 100 and b = 98 . Concept used: Linear approximation: If f is differentiable at x = a and Δ x is small, then - Δ f = f ' ( a ) Δ x Calculation: As per the given information, f ( x ) = 1 x , a = 100 and b = 98 . ∴ Δ x = b − a = 98 − 100 = − 2 . f ( x ) = 1 x = x − 1 2 ⇒ f ' ( x ) = − 1 2 x − 1 2 − 1 { Since, d d x ( x n ) = n x n − 1 } ⇒ f ' ( x ) = − 1 2 x − 3 2 ⇒ f ' ( 100 ) = − 1 2 ( 100 ) − 3 2 ⇒ f ' ( 100 ) = − 1 2000 Using linear approximation, Δ f = f ' ( a ) Δ x Δ f = f ' ( 100 ) Δ x Δ f = − 1 2000 × ( − 2 ) Δ f = 1 1000 Δ f = 0

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Chapter 4.1, Problem 16E

To determine

To estimate the value of Δf for a change in x from 100 to 98. The value of f(b) using linear approximation and error using calculator.

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Chapter 4.1, Problem 15E

Chapter 4.1, Problem 17E

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Chapter 4 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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To estimate the value of Δ f for a change in x from 100 to 98. The value of f ( b ) using linear approximation and error using calculator.

Solution Summary: The author calculates the value of Delta f using linear approximation and error using calculator.

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To estimate the value of Δf for a change in x from 100 to 98. The value of f(b) using linear approximation and error using calculator.

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Chapter 4 Solutions