Explanation Given information: f ( x ) = x 1 3 , a = 8 and b = 9 . 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 1 3 , a = 8 and b = 9 . ∴ Δ x = b − a = 9 − 8 = 1 . f ( x ) = x 1 3 ⇒ f ' ( x ) = 1 3 x 1 3 − 1 { Since, d d x ( x n ) = n x n − 1 } ⇒ f ' ( x ) = 1 3 x − 2 3 ⇒ f ' ( 8 ) = 1 3 ( 8 ) − 2 3 ⇒ f ' ( 8 ) = 1 12 Using

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 4.1, Problem 17E

To determine

To estimate the value of Δf for a change in x from 8 to 9. The value of f(b) using linear approximation and error using calculator.

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Chapter 4.1, Problem 16E

Chapter 4.1, Problem 18E

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Chapter 4 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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To estimate the value of Δ f for a change in x from 8 to 9. 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 8 to 9. The value of f(b) using linear approximation and error using calculator.

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