Explanation Given information: Following is the given information A function f ( x ) = sin x . Calculation: The instantaneous rate of change at the point x = π 6 for f ( x ) = sin x is the slope of the tangent line at x = π 6 . The slope of the secant line at x = π 6 is the same at the slope of the tangent line. Thus, the average rate of change of f ( x ) is equal to the instantaneous rate of change at the point x = π 6 . Δ f Δ x = f ( x 2 ) − f ( x 1 ) x 2 − x 1 Δ f Δ x = sin x 2 − sin x 1 x 2 − x 1 Now for the different intervals different values will get adjusted As we know π 6 = 180 ° 6 = 30 ° For the interval (30, 30.01), we get Δ f Δ x = sin ( 30.01 ) ° − sin ( 30 ) ° ( 30.01 ) ° − ( 30 ) ° Δ f Δ x = 0.015114 For the interval (30, 30.001), we get Δ f Δ x = sin ( 30.001 ) ° − sin ( 30 ) ° ( 30.001 ) ° − ( 30 ) ° Δ f Δ x = 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 2.1, Problem 17E

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Estimated instantaneous rate of change of f(x)=sinx at x=π6.

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Chapter 2.1, Problem 16E

Chapter 2.1, Problem 18E

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Chapter 2 Solutions

Calculus - Standalone book

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 5PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E

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Estimated instantaneous rate of change of f ( x ) = sin x at x = π 6 .

Solution Summary: The author calculates the instantaneous rate of change of f(x)=mathrmsinx, based on the slope of the tangent line and the

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Estimated instantaneous rate of change of f(x)=sinx at x=π6.

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Chapter 2 Solutions