In-class work for 14 June 2012
1.) Find the length of the space curve $\vec{r}(t) = < 2 \sin t, 5t, 2 \cos t >$ between $t=-10$ and $t=10$.

2.) Given $\vec{r}(t) = < \cos t, \sin t, 11t^2 >$, find the unit tangent, unit normal, and curvature. (lots of details for the "hard" part of this are on the solutions page)

3.) Find $\vec{T}$, $\vec{N}$, and $\vec{B}$ of the vector function $\vec{r}(t) = < \cos t, \sin t, \log \cos (t) >$ at the point $(1,0,0)$.

4.) Find the equation of the normal and osculating planes of the curve $$\left\{ \begin{array}{ll} x &= 2 \sin (3t) \\ y &= t \\ z &= 2 \cos (3t) \end{array} \right.$$ at the point $(0, \pi, -2)$.

5.) At what point on the curve $$\left\{ \begin{array}{ll} x &= t^2 \\ y &= 3t \\ z &= t^4 \end{array} \right.$$ is the normal plane parallel to the plane $6x+6y-8z=1$?