Math 128ASSIGNMENT 6Winter 2010Submit all problems by8:20 amonWednesday, March 3rdin the drop boxes across fromMC4066, or in class depending on your instructor’s preference.All solutions must beclearly statedandfully justified.1. Each of the following curves represents the path of a particle moving inR2. Make asketch of the curve, showing the direction of motion; then find the velocity and speed ofthe particle, and locate the points(x, y)at which the velocity is vertical or horizontal,or0. (Part d) not required).a)x(t) = (2 cost,3 sint),0≤t≤2πc)x(t) = (e-tcost, e-tsint),0≤t≤4πb)x(t) =t+1t, t-1t, t >0d)x(t) = (cos3t,sin3t),0≤t≤2π2. For each of the following curves, find the vector equation of the tangent line att0,and state the slope of the tangent line att0. Sketch the curve and tangent att0.[Note that the slope of a vectorv= (v1, v2) isv2/v1.]a)x(t) = (3t2, t3), t0=12b)x(t) = (sin2t,2 cost), t0=π/43. Find the total distance travelled by a particle along each of the following paths. Sketchthe paths.a)x(t) = (3t2, t3),-1≤t≤1b)x(t) = (cos3t,sin3t),0≤t≤2π4. A particle moving in a plane has position at time
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