(a) Is the following parametric surface regular: \rho: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3}, \quad \rho(u, v)=\left(u \cos v, u \sin v, u^{4}\right) ? Justify your answer. \text { b) Find the unit

normals at the point }(\sqrt{2},-\sqrt{2}, \sqrt{2}) \text { to the hyperboloid } \mathrm{H}=\left\{(x, y, z) \in \mathbb{R}^{3} \mid 4 z^{2}=x^{2}+y^{2}+4\right\} ) Let Q be the quarter-sphere, Q=\left\{(x, y, z) \in \mathbb{R}^{3} \mid x^{2}+y^{2}+z^{2}=1, x>0, y>0\right\} Describe the boundary of this surface Q, as one or more curves in R³. (You should express these curves as sets, or you can draw them for partial credit.) (d) Recall, from discussions in the lectures or lecture notes, that one can apply Green's theorem in order to express the area of an open region D CR² in terms of integrals over the boundary of D. Describe how one can similarly apply the divergence theorem to express the volume of an open region V C R in terms of an integral over the boundary of V.Here, you can suppose that the boundary of V is a single surface S.