I have the following limit:
I care for the case where $\epsilon>-1/2$. I suspect that for $\epsilon>0$ this limit evaluates to 1, and for $-1/2<\epsilon\leq0$ it evaluates to 0. However, I am having hard time evaluating this. I have tried taking the log of the expression (moving the $x$ in the exponent down), substituting $y=1/x$ and then Taylor-expanding the log, but didn't get anywhere.
Does anyone have any tips/hints that might help me evaluate this?