Explanation Given information: f ( x ) = cos x and n = 4 m + r where m is a whole number and r = 0 , 1 , 2 or 3 Formula Used: The derivative of the standard trigonometry function: d d x ( sin x ) = cos x and d d x ( cos x ) = − sin x Calculation: To calculate f ( n ) ( x ) for f ( x ) = cos x First, taking n = 4 m + r , let’s take m = 0 Then n = r i.e. n = 4 ( 0 ) + r = r Thus, f ( n ) ( x ) = f ( 4 m + r ) ( x ) = f ( r ) ( x ) Now for m = 0 and r = 0 f ( n ) ( x ) = f ( 4 m + r ) ( x ) = f ( 0 + 0 ) ( x ) = f ( 0 ) ( x ) = f ( x ) = sin x For m = 0 and r = 1 f ( n ) ( x ) = f ( 4 m + r ) ( x ) = f ( 0 + 1 ) ( x ) = f ( 1 ) ( x ) = d d x ( f ( x ) ) = d d x ( cos x ) = − sin x For m = 0 and r = 2 f ( n ) ( x ) = f ( 4 m + r ) ( x ) = f ( 0 + 2 )

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 3.6, Problem 46E

To determine

For f(x)=cosx , compute fn(x) by taking n=4m+r , where m is a whole number and r=0,1,2 or 3. Compute fn(x) from r and explain how to do latter step.

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Chapter 3.6, Problem 45E

Chapter 3.6, Problem 47E

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Chapter 3 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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For f ( x ) = cos x , compute f n ( x ) by taking n = 4 m + r , where m is a whole number and r = 0 , 1 , 2 or 3. Compute f n ( x ) from r and explain how to do latter step.

Solution Summary: The author explains how to compute fn(x) from r.

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For f(x)=cosx , compute fn(x) by taking n=4m+r , where m is a whole number and r=0,1,2 or 3. Compute fn(x) from r and explain how to do latter step.

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Chapter 3 Solutions