Chapter 12.3, Problem 75E

(a)

To determine

To find: Whether the statement, “the area of the region bounded by the polar graph of $r=f\left(\theta \right)$ on the interval $\left[\alpha ,\beta \right]$ is ${\displaystyle {\int }_{\alpha }^{\beta }f\left(\theta \right)d\theta }$” is true or false.

(b)

To determine

To find: Whether the statement, “the slope of the line tangent to the polar curve $r=f\left(\theta \right)$ at a point $\left(r,\theta \right)$ is $f^{\prime }\left(\theta \right)$” is true or false.

(c)

To determine

To find: Whether the statement, “there may be more than one line that is tangent to a polar curve at some points on the curve” is true or false.