Explanation Given information: f ( x ) = 1 x , a = 2 and b = 2.02 . 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 ) = 1 x , a = 2 and b = 2.02 . ∴ Δ x = b − a = 2.02 − 2 = 0.02 . Consider the function f ( x ) = 1 x = x − 1 ⇒ f ' ( x ) = − 1 x − 1 − 1 { Since, d d x ( x n ) = n x n − 1 } ⇒ f ' ( x ) = − x − 2 ⇒ f ' ( 2 ) = − ( 2 ) − 2 ⇒ f

4th Edition

ISBN: 9781319545956

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 22E

To determine

To find the linearization at x=2 and the value of f(b) using linear approximation.

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Chapter 4.1, Problem 21E

Chapter 4.1, Problem 23E

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Chapter 4 Solutions

CALCULUS W/ACHIEVE PLATFORM

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To find the linearization at x = 2 and the value of f ( b ) using linear approximation.

Solution Summary: The author calculates f(x) = 1x, a = 2 and b = 2.02 using linear approximation.

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To find the linearization at x=2 and the value of f(b) using linear approximation.

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Chapter 4 Solutions