Question

Let S be the surface z^2+x^2=1 with -17<=y<=7. Find a parameteriztion of the surface using the polar coordinates transformation equations z=Rcos(v), x=Rsin(v), and y=u, where u and v are parameters

Answer 1

The parameterization is already given to you, you just need to determine the domain for each parameter. $z^2+x^2=1$ is a cylinder that lies on the $y$-axis with radius 1. You need to take $0\le v\le2\pi$ to get the entire lateral face, and $-17\le u\le7$.