Another Limit Problem:

Compute the limit: $$\lim_{t \rightarrow \infty} \langle \arctan t, \frac{2^{-t}}{t}, \sin (e^{-2t}) \rangle$$

Derivatives:

Compute the derivative of the following functions:

• $$\cos x(1-\sin(e^{3x}))$$
• $$\sqrt{\cos^2(t^4)+\sin^2(t/2)}$$

Put it all together:

Find the derivative of the vector valued function: $$\mathbf{r}(t) = \langle \tan t, t \sec t, t^{3/2} \rangle$$