Math Models for Computer Science

1. Sketch the curve traced out by the tip of the vector function r(t) = (3cost)i -(4sint)j, where 0 t 2. (Assume r(t) is always in the standard position, i.e. with its initial point at the origin.) Indicate the direction in which the curve is traversed as t increases. [Review the topic of parametric curves from Calculus II.]

2. Find the first and second derivatives of f(t) = e^t costi - sin2tj + 3k.