Math 128 ASSIGNMENT 6 Winter 2009 Submit all problems by 8:20 am on Wednesday, March 4 th 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, or0 . (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 ² , 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 t0 , and state the slope of the tangent line at t0 . Sketch the curve and tangent at t0 . [Note that the slope of a vector
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