Problem 70
For the following equations, determine which of the conic sections is described. $$ x y=4 $$
Problem 70
Find the length of the curve \(x=e^{t}-t, y=4 e^{t / 2},-8 \leq t \leq 3\)
Problem 70
Without using technology, sketch the polar curve \(\theta=\frac{2 \pi}{3}\).
Problem 70
Find the points at which the following polar curves have a horizontal or vertical tangent line.\(r=4 \cos \theta\)
Problem 71
Find the points at which the following polar curves have a horizontal or vertical tangent line.\(r^{2}=4 \cos (2 \theta)\)
Problem 71
For the following equations, determine which of the conic sections is described. $$ x^{2}+4 x y-2 y^{2}-6=0 $$
Problem 71
Use a graphing utility to plot \(r=\theta \sin \theta\) for \(-\pi \leq \theta \leq \pi\).
Problem 71
For the following exercises, find the area of the surface obtained by rotating the given curve about the \(x\) -axis\(x=t^{3}, \quad y=t^{2}, \quad 0 \leq t \leq 1\)
Problem 72
Find the points at which the following polar curves have a horizontal or vertical tangent line.\(r=2 \sin (2 \theta)\)
Problem 72
Use technology to plot \(r=e^{-0.1 \theta}\) for \(-10 \leq \theta \leq 10\).
