Please show detailed work.

{a} If one wants to parametrize the portion of the graph ofa function :- _ 'I ll that is bounded by (right circular) cylinders (say, with the ..;-':r'-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: + 13; 2-,: 4 between the cylinders 1:1" I y2 1 and 3.1:" indicate the domain of your parametrization and provide a sketch of this surface. I y2 9. Clearly (b) Sketch and nd a parametrization for the portion of the surface given by lo; in the rst octant, clearly indicating the domain of your parametrization. Hint: notice that this is a surface of revolution because we can write can think of this surface as the one obtained by rotating a curve gl