91Ó°ÊÓ

Plot the point in polar coordinates and find the corresponding rectangular coordinates for the point. $$ (=3,=1.57) $$

Find the area of the region bounded by the graph of the polar equation using (a) a geometric formula and (b) integration.\(r=3 \cos \theta\)

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. \(x=2 t^{2}, \quad y=t^{4}+1\)

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. $$ \begin{array}{ll} \underline{\text { Parametric Equations }} & \underline{\text { Point }} \\ x=\sqrt{t}, y=3 t-1& \quad t=1 \end{array} $$

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. $$ \begin{array}{ll} \underline{\text { Parametric Equations }} & \underline{\text { Point }} \\ x=t+1, y=t^{2}+3 t &\quad t=-1 \end{array} $$

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. \(x=t^{3}, \quad y=\frac{t^{2}}{2}\)

Find the area of the region.One petal of \(r=2 \cos 3 \theta\)

Use the angle feature of a graphing utility to find the rectangular coordinates for the point given in polar coordinates. Plot the point. $$ (5,3 \pi / 4) $$

Find the area of the region.One petal of \(r=6 \sin 2 \theta\)

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. $$ \begin{array}{ll} \underline{\text { Parametric Equations }} & \underline{\text { Point }} \\ x=t^{2}+3 t+2, y=2 t &\quad t=0\end{array} $$