Chapter 10.5, Problem 79E

(a)

To determine

What happens to graph of $r=a\theta$ as $a$ increases and what happens if $\theta \le 0$.

(b)

To determine

To Calculate: The points on the spiral $r=a\theta \left(a>0,\theta \ge 0\right)$; where the curve crosses the polar axis

(c)

To determine

To Calculate: The Length of the curve $r=\theta$ over the interval $0\le \theta \le 2\pi$.

(d)

To determine

To Calculate: The area under the curve of the polar equation $r=\theta$ over the interval $0\le \theta \le 2\pi$