91Ó°ÊÓ

Finding the Area of a Polar Region In Exercises \(7-18\) , find the area of the region. Interior of \(r=3 \cos \theta\)

Polar-to-Rectangular Conversion In Exercises \(5-14,\) the polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. $$\left(0,-\frac{7 \pi}{6}\right)$$

Using Parametric Equations In Exercises \(5-22,\) sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$x=2 t^{2}, \quad y=t^{4}+1$$

Finding a Derivative In Exercises \(5-8,\) find \(d y / d x .\) $$x=2 e^{\theta}, \quad y=e^{-\theta / 2}$$

Using Parametric Equations In Exercises \(5-22,\) sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$x=t^{3}, \quad y=\frac{t^{2}}{2}$$

Polar-to-Rectangular Conversion In Exercises \(5-14,\) the polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. $$\left(7, \frac{5 \pi}{4}\right)$$

Finding the Area of a Polar Region In Exercises \(7-18\) , find the area of the region. One petal of \(r=2 \cos 3 \theta\)

Finding Slope and Concavity In Exercises \(9-18,\) find \(d y / d x\) and \(d^{2} y / d x^{2},\) and find the slope and concavity (if possible) at the given value of the parameter. $$\begin{array}{ll}{\text { Parametric Equations }} & {\text { Parameter }} \\\ {\text { 9. } x=4 t,} {y=3 t-2} & {t=3}\end{array}$$

Polar-to-Rectangular Conversion In Exercises \(5-14,\) the polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. $$\left(-2, \frac{11 \pi}{6}\right)$$

Using Parametric Equations In Exercises \(5-22,\) sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$x=t^{2}+t, \quad y=t^{2}-t$$