I’m currently attempting to take a limit of a function that involves little-o notation and was hoping someone could explain where I am going wrong.
After some manipulation I am left with the expression $$\exp(1/\varepsilon o_{\varepsilon\to 0}(1))=\exp(o_{\varepsilon\to 0}(1/\varepsilon))$$ I am now interested in what happens to this as $\varepsilon\to 0$. Does this not have a limit? Is there any way that I could control this limit? I thought this limit could be bounded between 1 and something else?
