Rapid Recall
1. Find the area of a parallelogram whose edges are the vectors $(a,b)$ and $(c,d)$.
Solution
2. For the curve $r=2\sin3\theta$, graph the curve in the $xy$ plane.
Solution
3. Give a vector equation of a line that passes through $(a,b)$ and is parallel to the vector $(c,d)$.
Solution
Group problems
- Consider the polar curve $r=\frac{2\theta}{\pi}$.
- Draw the curve (did you get a spiral) for $0\leq \theta\leq 4\pi$.
- Compute $\frac{dx}{d\theta}$ and $\frac{dy}{d\theta}$
- Set up an integral formula to calculate the length of the curve for $0\leq \theta\leq 2\pi$.
- Find the slope $dy/dx$ at $\theta=\pi$.
- Give an equation of the tangent line at $\theta = \pi$.
- Now swap the curve to $v=u^2$ and use the coordinates $x=2u+v$, $y=u-2v$. Then repeat the three parts above at $u=1$.
- Draw the curve in both the $uv$ and $xy$ planes.
- Find the slope $dy/dx$ at $u=1$.
- Give a vector equation of the tangent line to the curve in the $xy$ plane at $u=1$.
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