Problem 61
For the following exercises, find the arc length of the curve on the indicated interval of the parameter.\(x=\frac{1}{3} t^{3}, \quad y=\frac{1}{2} t^{2}, \quad 0 \leq t \leq 1\)
Problem 61
Sketch a graph of the polar equation and identify any symmetry. $$ r=3 \cos \left(\frac{\theta}{2}\right) $$
Problem 61
For the following exercises, sketch the graph of each conic. $$ r=\frac{3}{-4+2 \sin \theta} $$
Problem 62
For the following exercises, find the arc length of the curve on the indicated interval of the parameter.\(x=\cos (2 t), \quad y=\sin (2 t), \quad 0 \leq t \leq \frac{\pi}{2}\)
Problem 62
For the following exercises, find the slope of a tangent line to a polar curve \(r=f(\theta) .\) Let \(x=r \cos \theta=f(\theta) \cos \theta\) and \(y=r \sin \theta=f(\theta) \sin \theta\), so the polar equation \(r=f(\theta)\) is now written in parametric form.\(r=2 \sin (3 \theta) ;\) tips of the leaves
Problem 62
Sketch a graph of the polar equation and identify any symmetry. $$ r^{2}=4 \cos (2 \theta) $$
Problem 62
For the following exercises, sketch the graph of each conic. $$ \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 $$
Problem 63
Sketch a graph of the polar equation and identify any symmetry. $$ r^{2}=4 \sin \theta $$
Problem 63
For the following exercises, sketch the graph of each conic. $$ \frac{x^{2}}{4}+\frac{y^{2}}{16}=1 $$
Problem 63
For the following exercises, find the arc length of the curve on the indicated interval of the parameter.\(x=1+t^{2}, \quad y=(1+t)^{3}, \quad 0 \leq t \leq 1\)
