yet another limit question

Hi,

I have banged my head against this wall for hours:

I need to prove that the above is true, but without resorting to the theorem that limit of P(z) at a, where z and a are complex numbers, is P(a). nor do I want to use the theorem on limits of products or limit of two functions added together.

I basically want to construct a Delta that would make the following statement true:

I have tried a few different things:

1. translated to . I then calculated , then multiplied that by the final expression that needs to be bound by in order to get a factor that could somehow by bound by a constant. This would have allowed me to work forward from the expression involving to the final expression bound by .

2. Tried to work directly with the x's and y's

So far nothing has worked.

Any help would be much appreciated.