4. Determine whether the following set is open, connected, and/or simply-connected. Select all that apply.
\[
\left\{(x, y) \mid 1<x^{2}+y^{2}<9\right\}
\]
open
connected
simply-connected
5. Which of the following parametrizes a simple closed curve?
\( \vec{r}(t)=\langle 2 \sin t, 2 \cos t\rangle, 0 \leq t \leq 2 \pi \)
\( \vec{r}(t)=\langle 2 \sin t, 2 \cos t\rangle, 0 \leq t \leq 4 \pi \)
\( \vec{r}(t)=\langle 2 \sin t, 2 \cos t\rangle, 0 \leq t \leq \pi \)
All of these
None of these
6. Determine whether the vector field is conservative, and if so, find a potential function.
\[
\vec{F}(x, y)=\left\langle 3 x^{2}-2 y^{2}, 4 x y+3\right\rangle
\]
\( f(x, y)=x^{3}-2 x y^{2} \)
\( f(x, y)=x^{2}+2 x y^{2}+3 y \)
Not conservative
\( f(x, y)=2 x y^{2}+3 y \)
