Wolfram Alpha has choked on the following:
I feel powerless over the problem too. Any hints?
That's a lot of input for that online form. I'm having trouble with that also. However, on my copy of Mathematica, it evaluates the limit as in like half a second.
The way you'd go about proving this by hand would be to use L'Hopital's rule repeatedly, although judging by how contrived the example is, it might require a LOT of work. Maybe there is a smart way, I dunno.
You can also see that it diverges if you consider the order of every function. Since behaves as 1 near , we get that behaves like around . Similarly behaves like and behaves like . Also, behaves like around . If you use these you can see at least justify to yourself that the limit diverges.