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.
$$\lim_{n\rightarrow\infty} \frac{\sqrt{n}}{(\log(n))^2}$$
Best Answer
It's correct if the limit is infinity. The limit must exists, no matter if it is finite or not. On the other hand if you use l'Hopital rule and find that the limit does not exist you cannot conclude that the initial limit does not exist. In that case you must use another methods to analyse the limit.