Limit of the function as $\mu\rightarrow\infty$ or $\mu\rightarrow-\infty$ .

Question

$\lim_{\mu\rightarrow\infty}\frac{\exp(\bar x-\mu)^2}{(\bar x-\mu)}=? $

Also,

$\lim_{\mu\rightarrow-\infty}\frac{\exp(\bar x-\mu)^2}{(\bar x-\mu)}=? $

I know,

$\lim_{\mu\rightarrow\infty}\exp(\mu)=\infty$

and

$\lim_{\mu\rightarrow-\infty}\exp(\mu)=0$

Answer 1

Square of a negative number is positive. Exponent goes to infinity faster than any power.