Explanation Given information: An expression is given as, tan ( 0.04 ) . 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, tan ( 0.04 ) . Let us suppose, f ( x ) = tan x and a = 0 , b = 0.04 . We use the linearization of f ( x ) = tan x at a = 0 in approximation. ∴ Δ x = b − a = 0.04 − 0 = 0.04 . f ( x ) = tan x ⇒ f ' ( x ) = sec 2 x { Since, d d x ( tan x ) = sec 2 x } ⇒ f ' ( 0 ) = sec 2 ( 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.1, Problem 65E

To determine

The value of tan(0.04) using linear approximation.

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Chapter 4.1, Problem 64E

Chapter 4.1, Problem 66E

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The value of tan ( 0.04 ) using linear approximation.

Solution Summary: The author calculates the value of mathrmtan(0.04) using linear approximation.

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The value of tan(0.04) using linear approximation.

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