So if I've understood it correctly: 
lim x-> 0, lim y-> oo f(x) * g(y). We indeed have an indeterminate form of the type 0 · oo. There are several ways to solve like-wise indeterminations. The problem here is mainly the fact that we have independent variables. And not only that but functions of this variables that we don't know explicity how they behave. I would be interested what are your thoughts on the problem as I'm clueless to be honest.