Explanation Given information: f ( x ) = ( 1 + x ) − 1 2 , a = 0 and b = 0.08 . 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 ) − 1 2 , a = 0 and b = 0.08 . ∴ Δ x = b − a = 0.08 − 0 = 0.08 . Differentiate the function as follows: f ( x ) = ( 1 + x ) − 1 2 ⇒ f ' ( x ) = − 1 2 ( 1 + x ) − 1 2 − 1 × 1 { Using chain rule } ⇒ f ' ( x ) = − 1 2 ( 1 + x ) − 3 2 ⇒ f ' ( 0 ) = − 1 2 (

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Chapter 4.1, Problem 25E

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To find the linearization at x=0 and the value of f(b) using linear approximation.

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Chapter 4.1, Problem 24E

Chapter 4.1, Problem 26E

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Find the indefinite integral. Check Answer: 7x 4 + 1x dx

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Chapter 4 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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To find the linearization at x = 0 and the value of f ( b ) using linear approximation.

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