Explanation Given information: f ( x ) = tan ( x 4 + π 4 ) , a = 0 and Δ x = 0.01 . 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 ) = tan ( x 4 + π 4 ) , a = 0 and Δ x = 0.01 . f ' ( x ) = 1 4 sec 2 ( x 4 + π 4 ) { Since, d d x ( tan x ) = sec 2 x } ⇒ f ' ( 0 ) = 1 4 sec 2 ( 0 4 + π 4 ) ⇒ f ' ( 0 ) = 1 4 ( 2 ) 2 ⇒ f ' ( 0 ) = 1 2 Using linear approximation, Δ f = f ' ( a ) Δ x ⇒ Δ f = f ' ( 0 ) Δ x ⇒ Δ f = 1 2 × 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.1, Problem 12E

To determine

The value of Δf using linear approximation.

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Chapter 4.1, Problem 11E

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The value of Δ f using linear approximation.

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The value of Δf using linear approximation.

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