- Find the arc length of $\vec r(t) = (t^3,3t^2)$ for $t\in [1,3]$.
- Plot the polar points with $(r,\theta)$ given by $(2,0)$, $(2,\pi/6)$, $(-2,\pi/6)$, $(4,\pi/2)$, $(-4,\pi/2)$.
- Give a Cartesian equation of the polar curve $r=\frac{4}{3\sin\theta+2\cos\theta}$.
- Give a Cartesian equation of the polar curve $r=\tan\theta\sec\theta$.
- We know $x=r\cos\theta$ and $y=r\sin\theta$. Compute $dx$ in terms of $r, \theta,dr, d\theta$. (If you need to, assume that everything depends on $t$, compute derivatives, then multiply by $dt$.)
- Plot the curve $r=3-2\sin\theta$.
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