Explanation Given information: An expression is given as, cos ( 3.1 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: An expression is given as, cos ( 3.1 4 ) . Let us suppose, f ( x ) = cos x 4 and a = 3 , b = 3.1 . We use the linearization of f ( x ) = cos x 4 at a = 3 in approximation. ∴ Δ x = b − a = 3.1 − 3 = 0.1 . f ( x ) = cos x 4 ⇒ f ' ( x ) = − sin ( x 4 ) × 1 4 { Since, d d x ( c o s x ) = − sin x } ⇒ f ' ( x ) = − 1 4 sin ( x 4 ) ⇒ f ' ( a ) | a = 3 = − 1 4 sin ( 3 4 ) ⇒ f ' ( 3 ) = − 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.1, Problem 66E

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The value of cos(3.14) using linear approximation.

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Chapter 4.1, Problem 65E

Chapter 4.1, Problem 67E

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Chapter 4 Solutions

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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 cos ( 3.1 4 ) using linear approximation.

Solution Summary: The author calculates the value of mathrmcos(3.14) using linear approximation.

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