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: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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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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For the following function f and real number a, a. find the slope of the tangent line mtan = f' (a), and b. find the equation of the tangent line to f at x = a. f(x)= 2 = a = 2 x2 a. Slope: b. Equation of tangent line: y

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Chapter 4 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

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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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