(a) If one wants to parametrization of the graph of a function z = f(@, y) that is bounded by (right circular) cylinders (say, with the z-axis as the rotation axis), one usually uses cylindrical coordinates. For instance, use cylindrical coordinates to find a parametrization for the portion of the the plane x + 4y + 2z = 4 between the cylinders a2 + y = 1 and x2 + y = 9. Clearly indicate the domain of your parametrization and provide a sketch of this surface. (b) Sketch and find a parametrization for the portion of the surface given by log(y) = vx2 + z in the first octant, clearly indicating the domain of your parametrization. Hint: notice that this is a surface of revolution because we can write x2 + z? = f(y) for a suitable function f. This means that we can think of this surface as the one obtained by rotating a curve g(y, z) = 0 on the yz-plane about the y-axis. The first octant condition means that x, y, z 2 0