Explanation Given information: f ( x ) = sin x x , a = π 4 . 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 ) = sin x x , a = π 4 . ∴ Δ x = ( b − a ) . f ( x ) = sin x x ⇒ f ' ( x ) = x cos x − sin x x 2 { Using quotient rule, d d x ( u v ) = v d u d x − u d v d x u 2 } ⇒ f ' ( π 4 ) = x cos x − sin x x 2 ⇒ f ' ( π 4 ) = π 4 cos π 4 − sin π 4 ( π 4 ) 2 ⇒ f ' ( π 4 ) = π 4 1 2 − 1 2 ( π 4 ) 2 ⇒ f ' ( π

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 26E

To determine

The value of f(b) using linear approximation.

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Chapter 4.1, Problem 25E

Chapter 4.1, Problem 27E

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Chapter 4 Solutions

CALCULUS (CLOTH)

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