I am having trouble expressing the behavior of the following limit:
After some simple arithmetic manipulations I can simplify this expression to this:
with the following constraints on the parameters: $0<b<a<\infty$, and $-0.5<\epsilon<0.5$. For $0<\epsilon<0.5$ it seems to go to zero, and for $-0.5<\epsilon<0$ it seems to go to one (at least it looks that way when plotting it in MATLAB, see pictures for $a=1$, $b=0.1$.) At $\epsilon=0.5$ it's a constant function of $a$ and $b$, according to an answer to my previous and related question.
I am perplexed on how to actually prove the statements for $0<\epsilon<0.5$ and $-0.5<\epsilon<0$. It'd be great if someone could help!