Explanation Given: 1 15 f ( x ) = 1 x Concepts: 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: Write the nearest perfect square to 15 Write the nearest perfect square to 15 is 16 Step 2: Find f ' ( x ) Let f ( x ) = 1 x and a = 16 Then f ' ( x ) = 1 2 x − 3 / 2 and f ' ( a ) = f ' ( 16 ) =

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Linear Correlation

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Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Question

Chapter 4.1, Problem 56E

To determine

Whether the given estimate from the Linear Approximation is too large or too small and use calculator to compute the percentage error

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Chapter 4.1, Problem 55E

Chapter 4.1, Problem 57E

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Chapter 4 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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Whether the given estimate from the Linear Approximation is too large or too small and use calculator to compute the percentage error

Solution Summary: The author explains the linear approximation of y = f(x) at the point (a,f)

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Whether the given estimate from the Linear Approximation is too large or too small and use calculator to compute the percentage error

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Chapter 4 Solutions