Hi guys. I have two questions.

For #1:

f(x) = x ^ (1/x)

a) What is the domain of f(x)?

b) Determine (with justification) the lone horizontal asymptote of the graph y = f(x).

For a, I believe the answer is x > 0.

For b, I'm guessing that you derive the equation and set it to 0?

For #2:

Let R be the region under the curve y = sin (x) and above the x-axis between x = 2pi and x = 3pi. Find the volume generated by rotating R about the line x = -2.

For this one, I believe that this is one of those shell, disk, or washer problems. I'm not quite sure on which to use, but it looks to me like it may be shell. However, I have some trouble setting up my shell integral.