- Draw the curve $r=2+2\sin\theta$ in the $xy$ plane.
- We have already seen that $dx = \cos\theta dr-r\sin\theta d\theta$ and $dy = \sin\theta dr+r\cos\theta d\theta$. Use this information to compute the slope $dy/dx$ of the previous curve at $\theta= \pi$. (You should end up with -1.)
- Give a vector equation of the tangent line to the curve above 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 $u=1$.
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