138assgn10

138assgn10 - MATH 138 Assignment 10 Spring 2009...

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Unformatted text preview: MATH 138 Assignment 10 Spring 2009 Vector-valued functions. 1. Sketch and identify the curve. (a) F ( t ) = (1 + t, 5- 2 t ) ,- 2 t 3. (b) F ( t ) = ( t 2- 2 , 5- 2 t ) ,- 3 t 4. (c) F ( t ) = (1 + 3 t, 2- t 2 ). (d) F ( t ) = ( t, 1- t ). 2. Eliminate the parameter to find a Cartesian equation of the curve. Sketch the curve. of conver- gence. (a) x = e t- 1 , y = e 2 t . (b) F ( t ) = ( e 2 t , t + 1). (c) F ( t ) = (ln t, t ) , t 1. 3. Describe the motion of a particle with position ( x, t ) as t varies in the given interval. (a) x = 2 sin t, y = 4 + cos t, t 3 / 2. (b) x = 5 sin t, y = 2 cos t,- t 5 . (c) x = sin t, y = cos 2 t,- 2 t 2 . 4. Compare the curves represented by the parametric equations. How do they differ? (a) x ( t ) = t y ( t ) = t- 1 . (b) x ( t ) = e t y ( t ) = e- 2 t . (c) x ( t ) = cos t y ( t ) = sec 2 ( t )....
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138assgn10 - MATH 138 Assignment 10 Spring 2009...

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