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

4th Edition

ISBN: 9781319545956

Author: Rogawski

Publisher: MAC HIGHER

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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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5) Linearize f(x) for a given value of a and use it to approximate a given value of b. Show your calculations. Compare your result with calculator value.

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Chapter 4 Solutions

CALCULUS W/ACHIEVE PLATFORM

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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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