91影视

Determine a definite integral that represents the area.Region in the first quadrant enclosed by \(r=2-\cos \theta\)

Sketch the parametric equations by eliminating the parameter. Indicate any asymptotes of the graph. $$ x=3-2 \cos \theta, \quad y=-5+3 \sin \theta $$

Find the surface area generated when the plane curve defined by the equations $$ x(t)=t^{3}, \quad y(t)=t^{2}, \quad 0 \leq t \leq 1 $$ is revolved around the \(x\) -axis.

Determine the eccentricity of the hyperbola described by the equation $$ \frac{(y-3)^{2}}{49}-\frac{(x+2)^{2}}{25}=1 $$

Plot the point whose polar coordinates are given by first constructing the angle \(\theta\) and then marking off the distance \(r\) along the ray. $$ \left(-2, \frac{5 \pi}{3}\right) $$

Plot the point whose polar coordinates are given by first constructing the angle \(\theta\) and then marking off the distance \(r\) along the ray. $$ \left(0, \frac{7 \pi}{6}\right) $$

Sketch the parametric equations by eliminating the parameter. Indicate any asymptotes of the graph. $$ x=4+2 \cos \theta, \quad y=-1+\sin \theta $$

Determine a definite integral that represents the area.Region enclosed by the inner loop of \(r=2-3 \sin \theta\)

For the following exercises, each set of parametric equations represents a line. Without eliminating the parameter, find the slope of each line.\(x=3+t, \quad y=1-t\)

For the following exercises, each set of parametric equations represents a line. Without eliminating the parameter, find the slope of each line.\(x=8+2 t, \quad y=1\)