(a) On a separate sheet of paper, sketch the parameterized curve $x=t \cos t, \ y=t \sin t$ for $0 \leq t \leq 4\pi$. Use your graph to complete the following statement:
At $t = 2.5$, a particle moving along the curve in the direction of increasing $t$ is moving ? up down neither up nor down and ? to the left to the right neither to the left nor to the right

(b) By calculating the position at $t = 2.5$ and $t=2.51$, estimate the speed at $t=2.5$.
speed $\approx$

(c) Use derivatives to calculate the speed at $t=2.5$ and compare your answer to part (b).
speed =