Q:

Find $\lim\limits_{n→∞}\left(t+\frac{x}{n}\right)^n$

How would one go about finding the limit of $\displaystyle \left(|t|+\frac{x}{n}\right)^n$ as $n\rightarrow\infty$? ( $t$ and $x$ are both positive.) 
Of course $\displaystyle \left(1+\frac{x}{n}\right)^n$ has limit $e^x$, but how would this help? 

A:

Use:
$$\lim\limits_{n→∞}\left(1+\frac{Q}{n}\right)^n=e^Q$$
So you have:
$$\lim\limits_{n→∞}\left(t+\frac{x}{n}\right)^n=\lim\limits_{n→∞}\left(1+\frac{{x\over t}}{n}\right)^n*t^n=e^{x\over t}*t^n$$
The limit is:
∞ if $t>1$
 0 if $t<1$
$e^{x\over t}$ if $t=1$    

