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Assign6 - Math 128 ASSIGNMENT 6 Winter 2010 Submit all...

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Math 128 ASSIGNMENT 6 Winter 2010 Submit all problems by 8:20 am on Wednesday, March 3 rd in the drop boxes across from MC4066, or in class depending on your instructor’s preference. All solutions must be clearly stated and fully justified . 1. Each of the following curves represents the path of a particle moving in R 2 . Make a sketch of the curve, showing the direction of motion; then find the velocity and speed of the particle, and locate the points ( x, y ) at which the velocity is vertical or horizontal, or 0 . (Part d) not required). a) x ( t ) = (2 cos t, 3 sin t ) , 0 t 2 π c) x ( t ) = ( e - t cos t, e - t sin t ) , 0 t 4 π b) x ( t ) = t + 1 t , t - 1 t , t > 0 d) x ( t ) = (cos 3 t, sin 3 t ) , 0 t 2 π 2. For each of the following curves, find the vector equation of the tangent line at t 0 , and state the slope of the tangent line at t 0 . Sketch the curve and tangent at t 0 . [Note that the slope of a vector v = ( v 1 , v 2 ) is v 2 /v 1 .] a) x ( t ) = (3 t 2 , t 3 ) , t 0 = 1 2 b) x ( t ) = (sin 2 t, 2 cos t ) , t 0 = π/ 4 3. Find the total distance travelled by a particle along each of the following paths. Sketch the paths. a) x ( t ) = (3 t 2 , t 3 ) , - 1 t 1 b) x ( t ) = (cos 3 t, sin 3 t ) , 0 t 2 π 4. A particle moving in a plane has position at time
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