- Given an equation of the tangent line to the curve $\vec r(t) = (t^2, t^3)$ at $t=2$.
- An object travels along straight lines. It's velocity is $ (0,3,4) $ for 2 seconds, and then turns so it's velocity is $ (1,2,-2) $ for 5 seconds. What is the distance traveled by the object.
- Find the arc length of the curve $\vec r(t) = (t^2, t^3)$ for $0\leq t\leq 2$.
- Consider the ray from the origin through the point $P=(-2,2)$. What's the angle between this ray and the positive $x$ axis? What the distance from the origin to $P$?
- Repeat the previous problem, but now with $P=(-3,4)$.
- Repeat the previous problem, but now with $P=(x,y)$.
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