Explanation Given information: f ( x ) = x 1 3 , a = 27 and b = 30 . 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 3 , a = 27 and b = 30 . ∴ Δ x = b − a = 30 − 27 = 3 . f ( x ) = x 1 3 ⇒ f ' ( x ) = 1 3 x 1 3 − 1 { Since, d d x ( x n ) = n x n − 1 } ⇒ f ' ( x ) = 1 3 x − 2 3 ⇒ f ' ( 27 ) = 1 3 ( 27 ) − 2 3 ⇒ f ' ( 27 ) = 1 27 = 0

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 18E

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Chapter 4.1, Problem 17E

Chapter 4.1, Problem 19E

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Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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The value of f ( b ) using linear approximation and error using calculator.

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Chapter 4 Solutions