Domains:

What is the domain of the following vector functions:

• $$\mathbf{r}(t) = \langle \sqrt{9 - t}, \tan t, t^2\rangle$$
• $$\mathbf{r}(t) = \langle (t^2-3)^{3/2}, \ln (t-1), \frac{t-2}{t+2} \rangle$$

Limits:

Find the limit:

$$\lim_{t \rightarrow 0} \langle \frac{e^t-1}{t}, \frac{\sqrt{1-t^3} - 1}{t^3},\frac{\sin t}{t} \rangle$$

Lines (review):

Find a vector equation and parametric equations for the line segment that joints $(1,0,1)$ to $(2,3,1)$.