Explanation Given: The graphs: The parametric equations. (a) c ( t ) = ( sin t , − t ) (b) c ( t ) = ( t 2 − 9 , 8 t − t 3 ) (c) c ( t ) = ( 1 − t , t 2 − 9 ) (d) c ( t ) = ( 4 t + 2 , 5 − 3 t ) Calculation: (a) The curve c ( t ) = ( sin t , − t ) correspond to plot (1V) as the x coordinate ( sin t ) of the curve varies between − 1 to 1 . Also the y coordinate ( − t ) is decreasing. Hence, the direction of motion is downward. (b) Since c ( t ) = ( t 2 − 9 , 8 t − t 3 ) intersects the x axis when y ( t ) =0 that is,, 8 t − t 3 = 0 t ( 8 − t 2 ) = 0 t = 0 and t 2 = 8 t = 0 and t = ± 2 2 Therefore the points are ( ( 2 2 ) 2 − 9 , 0 ) and ( 0 2 − 9 , 0 ) ( 8 − 9 , 0 ) and ( − 9 , 0 ) ( − 1 , 0 ) and ( − 9 , 0 ) The y intercepts are obtained when x ( t ) = 0 t 2 − 9 = 0 t = ± 3 The y intercepts are ( 0 , 8 × 3 − ( 3 ) 3 ) and ( 0 , 8 × ( − 3 ) − ( − 3 ) 3 ) ( 0 , 24 − 27 ) and ( 0 , − 24 + 27 ) ( 0 , − 3 ) and ( 0 , 3 ) As t increases from − ∞ to 0 , x decreases, and as t increases from 0 to ∞ , x increases...

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ISBN: 9781319050733

Author: Rogawski

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Chapter 12.1, Problem 19E

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The matching of parametrization with their plots given in figure and draw an arrow indicating the direction of motion.

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Chapter 12.1, Problem 18E

Chapter 12.1, Problem 20E

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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 matching of parametrization with their plots given in figure and draw an arrow indicating the direction of motion.

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The matching of parametrization with their plots given in figure and draw an arrow indicating the direction of motion.

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