Provide an Appropriate Response $\mathrm { r } = \mathrm { f } ( \theta )$

question 152

Essay

Provide an appropriate response.
-Assuming $\mathrm { r } = \mathrm { f } ( \theta )$ is continuous for $\alpha \leq \theta \leq \beta$ and $\alpha < \beta \leq \alpha + 2 \pi$ , what can be said about the relative areas betweel the origin and the polar curves and
$\begin{array} { l } \mathrm { r } = \mathrm { f } ( \theta ) , \quad \alpha \leq \theta \leq \beta \\\mathrm { r } = 2 \mathrm { f } ( \theta ) , \quad \alpha \leq \theta \leq \beta ?\end{array}$
Give reasons for your answer.

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