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

Question 199

Essay

Provide an appropriate response.
-Assuming r=f(θ)\mathrm { r } = \mathrm { f } ( \theta ) is continuous for αθβ\alpha \leq \theta \leq \beta and α<βα+2π\alpha < \beta \leq \alpha + 2 \pi , what can be said about the relative areas betweel the origin and the polar curves and
r=f(θ),αθβr=2f(θ),αθβ?\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.

Correct Answer:

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The area between the origin an...

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