7. Given that a(t) = (cost, 2sint) with initial velocity u = (0, 1) and intial position "(0) = (1, 0) describe the trajectory of a particle. Carefully derive the following. [12 pts] a) Find the velocity vector function. b) Find the position vector function. c) Find the velocity when the particle is at position (3/2, x - V3)8. Find lim if it exists or show it doesn't exist. Show your work carefully.[7pts] (I,y) + (0,0)