91Ó°ÊÓ

Find the lengths of the curves. $$\text { The parabolic segment } r=6 /(1+\cos \theta), \quad 0 \leq \theta \leq \pi / 2$$

Graph the sets of points whose polar coordinates satisfy the equations and inequalities in Exercises \(11-26\). $$-\pi / 2 \leq \theta \leq \pi / 2, \quad 1 \leq r \leq 2$$

Find the lengths of the curves $$x=t^{3}, \quad y=3 t^{2} / 2, \quad 0 \leq t \leq \sqrt{3}$$

Graph the sets of points whose polar coordinates satisfy the equations and inequalities in Exercises \(11-26\). $$0 \leq \theta \leq \pi / 2, \quad 1 \leq|r| \leq 2$$

Graph the limaçons in Exercises. Limaçon ("lee-ma-sahn") is Old French for "snail." You will understand the name when you graph the limaçons in Exercise \(25 .\) Equations for limaçons have the form \(r=a \pm b \cos \theta\) or \(r=a \pm b \sin \theta .\) There are four basic shapes. Cardioids a. \(r=1-\cos \theta\) b. \(r=-1+\sin \theta\)

Find the lengths of the curves. $$\text { The parabolic segment } r=2 /(1-\cos \theta), \quad \pi / 2 \leq \theta \leq \pi$$

Replace the polar equations in Exercises \(27-52\) with equivalent Cartesian equations. Then describe or identify the graph. $$r \cos \theta=2$$

Find the lengths of the curves $$x=t^{2} / 2, \quad y=(2 t+1)^{3 / 2} / 3, \quad 0 \leq t \leq 4$$

Find the lengths of the curves. $$\text { The curve } r=\cos ^{3}(\theta / 3), \quad 0 \leq \theta \leq \pi / 4$$

Graph the limaçons in Exercises. Limaçon ("lee-ma-sahn") is Old French for "snail." You will understand the name when you graph the limaçons in Exercise \(25 .\) Equations for limaçons have the form \(r=a \pm b \cos \theta\) or \(r=a \pm b \sin \theta .\) There are four basic shapes. Dimpled limaçons a. \(r=\frac{3}{2}+\cos \theta\) b. \(r=\frac{3}{2}-\sin \theta\)