91Ó°ÊÓ

Find \(d y / d x\) and \(d^{2} y / d x^{2} .\) For which values of \(t\) is the curve concave upward? $$x=\cos 2 t, \quad y=\cos t, \quad 0

\(9-16=(\) a) Find the eccentricity, (b) identify the conic, (c) give an equation of the directrix, and (d) sketch the conic. $$ r=\frac{3}{2+2 \cos \theta} $$

Sketch the curve and find the area that it encloses. $$r=4+3 \sin \theta$$

Identify the curve by finding a Cartesian equation for the curve. $$r=2 \cos \theta$$

\(9-16=(\) a) Find the eccentricity, (b) identify the conic, (c) give an equation of the directrix, and (d) sketch the conic. $$ r=\frac{9}{6+2 \cos \theta} $$

Graph the curve and find the area that it encloses. $$r=\sqrt{1+\cos ^{2}(5 \theta)}$$

\(9-14=\) (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. $$x=e^{2 t}, \quad y=t+1$$

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. $$x=t^{3}-3 t, \quad y=t^{2}-3$$

\(9-16=(\) a) Find the eccentricity, (b) identify the conic, (c) give an equation of the directrix, and (d) sketch the conic. $$ r=\frac{5}{2-2 \sin \theta} $$

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. $$ x=t^{3}-3 t, \quad y=t^{3}-3 t^{2} $$