Section 13.3 – Arc Length and Curvature
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Find the length of the curve \(\mathbf{r}(t) = \langle 3\cos(t), 3\sin(t), 2t \rangle\) from \((3,0,0)\) to \((-3,0,2\pi).\)
\(\sqrt{13}\pi\)
2. Find the curvature of \(\mathbf{r}(t) = \left< t, t^2, t^3 \right>\) at the point \((1,1,1).\)
\(\dfrac{\sqrt{76}}{14^{3/2}}\)