See if you understand how to parametrize surfaces in R^3.

(a) If one wants to parametrlze the portion of the graph of a function 2 : x, 3;) 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 nd a parametrization for the portion of the the plane :1: + 4y + 2.: = 4 between the cylinders {C2 + y2 = 1 and m2 + y2 = 9. Clearly indicate the domain of your parametrization and provide a sketch of this surface. (b) Sketch and nd a parametrization for the portion of the surface given by 10g(y} : V 1'2 + 22 in the rst octant, clearly indicating the domain of your parametrization. Hint: noce that this is a surface of revolution because we can write 12 + 22 : 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 rst octant condition means that z, y, z 2 Cl