Rewrite solution

Couple of things.

Part (a) mentions nothing about the domain of f and so some discussion on this must be included here.

Then the solution shouldn't use L'Hopital's Rule I don't think (You can move it to solution 2 however)... though to be honest I don't know how this should be solved... The hint in the question is either wrong or there is some other trick that I'm missing. In anycase I don't think they know L'Hopital's Rule (at least traditionally) so perhaps the first solution should just be that exponentials grow faster than polynomials and so the limit is infinite.