Finding the behavior of coth(x) as T approaches 0 and infinity

[subzero0137]

1

The attempt at a solution:

For part a) I got the following:

I'm stuck on part b). I've tried to take the maclaurin series of coth x to see what the function does when T→0 and T→∞

 

[mfb]

I've tried to take the maclaurin series of coth x to see what the function does when T→0 and T→∞

What was the result of this?