Explanation Given: c ( t ) = ( sin t + t , cos t + t ) . Calculation: It is given that c ( t ) = ( sin t + t , cos t + t ) that means we have x ( t ) = sin t + t , y ( t ) = cos t + t Now, differentiate both the equations x ( t ) = sin t + t , y ( t ) = cos t + t with respect to t and we get: x ( t ) = sin t + t , y ( t ) = cos t + t d x d t = 1 + cos t , d y d t = 1 − sin t So, ( d x d t ) 2 + ( d y d t ) 2 = ( 1 + cos t ) 2 + ( 1 − sin t ) 2 = 1 + cos 2 t + 2 cos t + 1 + sin 2 t − 2 sin t = 2 + ( sin 2 t + cos 2 t ) + 2 ( cos t − sin t ) = 3 + 2 ( cos t − sin t ) So, the speed of the particle whose position at time t is given by: Speed = d s d t = ( d x d t ) 2 + ( d y d t ) 2 d s d t = 3 + 2 ( cos t − sin t ) When the expression ( cos t − sin t ) obtains maximum value then the speed will be the maximum...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 12, Problem 21CRE

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The speed of a particle whose position at time t seconds is $c (t) = (\sin t + t, \cos t + t)$ and to determine the particle’s maximum speed

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Chapter 12, Problem 20CRE

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Chapter 12 Solutions

CALCULUS (CLOTH)

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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The speed of a particle whose position at time t seconds is $c (t) = (\sin t + t, \cos t + t)$ and to determine the particle’s maximum speed