# L'Hospital Rule: Requirement that the limit exists

Could someone define what it means for a limit to "exist"?

Must the limit after using L'Hospital Rule approach a specific value?

What if the limit after using L'Hospital Rule approaches infinity? Does it count as being existent?

i.e.

$$\lim_{n\rightarrow\infty} \frac{\sqrt{n}}{(\log(n))^2}$$