Explanation Given: f ( x ) = x a t x = 9 | f ' ' ( x ) | ≤ K f o r x ≥ 9 Concept: Suppose that y = f ( x ) is a differentiable curve at x = a . Then the tangent line at x = a has equation y = f ( a ) + f ' ( a ) ( x − a ) We call the above equation the linear approximation or linearization of y = f ( x ) at the point ( a , f ( a ) ) and write f ( x ) ≈ L ( x ) = f ( a ) + f ' ( a ) ( x − a ) We sometimes write L a ( x ) to stress that the approximation is near a . Calculation: Description Step 1: Find f ' ( x ) Let f ( x ) = x Then f ( 9 ) = 3 , f ' ( x ) = 1 2 x − 1 / 2 and f ' ( a ) = f ' ( 9 ) = 1 6 Step 2: By linear approximation, we will get… f ( 9 + h ) − f ( 9 ) = 9 + h − 3 ≈ 1 6 h Moreover, f ' ' ( x ) = −<

4th Edition

ISBN: 9781319545956

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 67E

To determine

The Linear Approximation to the given function yields the given estimate and to verify that the error numerically satisfies the given equation.

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Chapter 4.1, Problem 66E

Chapter 4.1, Problem 68E

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Chapter 4 Solutions

CALCULUS W/ACHIEVE PLATFORM

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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The Linear Approximation to the given function yields the given estimate and to verify that the error numerically satisfies the given equation.

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