Help: Minor detail in proof of uniform convergence

The problem states:

Prove that the following limit exists and find the limit.

I've already shown that the pointwise limit is 1, but when I try to show that it converges uniformly using the definition that

If

then it's uniformly convergent, I run into a slight problem... I get to a point where I have

and I want to show (after a few more inequalities) that this is less than epsilon.

However, how can I account for the fact that sometimes the is negative, thus giving me a nonreal value?

What this all boils down to, is can I say that