Explanation Given information: f ( x ) = x , a = 25 and b = 26 . 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 ) = x , a = 25 and b = 26 . ∴ Δ x = b − a = 26 − 25 = 1 And f ( x ) = x = x 1 2 ⇒ f ' ( x ) = 1 2 x 1 2 − 1 { Since, d d x ( x n ) = n x n − 1 } ⇒ f ' ( x ) = 1 2 x − 1 2 ⇒ f ' ( 25 ) = 1 2 ( 25 ) − 1 2

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.1, Problem 13E

To determine

To estimate the value of Δf for a change in x from 25 to 26.The value of f(b) using linear approximation and error using calculator.

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Chapter 4.1, Problem 12E

Chapter 4.1, Problem 14E

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Chapter 4 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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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To estimate the value of Δ f for a change in x from 25 to 26.The value of f ( b ) using linear approximation and error using calculator.

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To estimate the value of Δf for a change in x from 25 to 26.The value of f(b) using linear approximation and error using calculator.

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