In Exercises 23 to 40, solve each equation.

Math 113 β Calculus III Exam 3 Practice Problems Fall 2005 1. Suppose the motion of a particle is given by x = 4cost, y = sint. (a) Describe the motion of the particle, and sketch the curve along which the particle travels. (b) Find the velocity and acceleration vectors of the particle. (c) Find the times t and the points on the curve where the speed of the particle is greatest. (d) Find the times t and the points on the curve where the magnitude of the acceler- ation is greatest. 2. Find the coordinates of the points where the line x = t, y = 1 + t, z = 5t intersects the surface