91影视

Use the integration capabilities of a calculator to approximate the length of the curve.[T] \(r=\frac{2}{\theta}\) on the interval \(\pi \leq \theta \leq 2 \pi\)

For the following exercises, consider the following polar equations of conics. Determine the eccentricity and identify the conic. $$ r=\frac{-1}{1+\cos \theta} $$

The pairs of parametric equations represent lines, parabolas, circles, ellipses, or hyperbolas. Name the type of basic curve that each pair of equations represents. $$ \begin{aligned} &x=2 \cos (3 t) \\ &y=2 \sin (3 t) \end{aligned} $$

Describe the graph of each polar equation. Confirm each description by converting into a rectangular equation. $$ r=\sec \theta $$

For the following exercises, find points on the curve at which tangent line is horizontal or vertical.\(x=t\left(t^{2}-3\right), \quad y=3\left(t^{2}-3\right)\)

The pairs of parametric equations represent lines, parabolas, circles, ellipses, or hyperbolas. Name the type of basic curve that each pair of equations represents. $$ \begin{aligned} &x=\cosh t \\ &y=\sinh t \end{aligned} $$

For the following exercises, consider the following polar equations of conics. Determine the eccentricity and identify the conic. $$ r=\frac{8}{2-\sin \theta} $$

For the following exercises, find points on the curve at which tangent line is horizontal or vertical.\(x=\frac{3 t}{1+t^{3}}, \quad y=\frac{3 t^{2}}{1+t^{2}}\)

Describe the graph of each polar equation. Confirm each description by converting into a rectangular equation. $$ r=\csc \theta $$

For the following exercises, find \(d y / d x\) at the value of the parameter.\(x=\cos t, \quad y=\sin t, \quad t=\frac{3 \pi}{4}\)