Explanation Given information: f ( x ) = x 1 4 , a = 16 and b = 16.5 . 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 ) = x 1 4 , a = 16 and b = 16.5 . ∴ Δ x = b − a = 16.5 − 16 = 0.5 And f ( x ) = x 1 4 ⇒ f ' ( x ) = 1 4 x 1 4 − 1 { Since, d d x ( x n ) = n x n − 1 } ⇒ f ' ( x ) = 1 4 x − 3 4 ⇒ f ' ( 16 ) = 1 4 ( 16 ) − 3 4 ⇒ f ' ( 16 ) = 1 32 Using linear approximation, Δ f = f ' ( a ) Δ x = f ' ( 16 ) Δ x = 1 32 × 0

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.1, Problem 14E

To determine

To estimate the value of Δf for a change in x from 16 to 16.5. The value of f(b) using linear approximation and error using calculator.

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Chapter 4.1, Problem 13E

Chapter 4.1, Problem 15E

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Chapter 4 Solutions

Calculus: Early Transcendentals

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To estimate the value of Δ f for a change in x from 16 to 16.5. The value of f ( b ) using linear approximation and error using calculator.

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To estimate the value of Δf for a change in x from 16 to 16.5. The value of f(b) using linear approximation and error using calculator.

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