What is $\lim\limits_{n\to\infty}\frac{x}{n(1-(1-x/n)e^{t/n})}$ I'm interested in finding this limit, and while I can plug it into Wolfram and have it spit out $\frac{x}{x-t}$ for me, I'm interested in how to "do" this limit.
I'd post my efforts, but I honestly haven't really been able to get farther than
\begin{align*}
\displaystyle\lim_{n\to\infty}\dfrac{x}{n\left(1-\left(1-\dfrac{x}{n}\right)e^{t/n}\right)}=\lim_{n\to\infty}\frac{x}{n-ne^{t/n}+xe^{t/n}}
\end{align*}
If anyone could point me in the right direction, that'd be cool. I'm just curious!

Hint
Just consider $$A=\frac{x}{n\left(1-\left(1-\frac{x}{n}\right)e^{t/n}\right)}$$ and now use the fact that, for small $y$ $$e^y=1+y+\frac{y^2}{2}+O\left(y^3\right)$$ Replace $y$ by $\frac tn$ and simplify.
I am sure that you can take from here.
