Explanation Given information: f ( x ) = ( 1 + x ) − 1 2 , a = 0 and b = 0.08 . 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 ) − 1 2 , a = 0 and b = 0.08 . ∴ Δ x = b − a = 0.08 − 0 = 0.08 . f ( x ) = ( 1 + x ) − 1 2 ⇒ f ' ( x ) = − 1 2 ( 1 + x ) − 1 2 − 1 × 1 { Using chain rule } ⇒ f ' ( x ) = − 1 2 ( 1 + x ) − 3 2 ⇒ f ' ( 0 ) = − 1 2

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.1, Problem 23E

To determine

The value of f(b) using linear approximation.

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Chapter 4.1, Problem 22E

Chapter 4.1, Problem 24E

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Chapter 4 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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.

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Chapter 4 Solutions