There is a regular stream of questions asking for limits by elementary means - "without l'Hopital" (I've omitted the accent) - would this be a viable tag for questions?
My doubt is that it simply won't be used because people won't imagine such a thing could exist. On the other hand it would gather together a collection of similar questions, and might assist in the identification of duplicates.
Having read comments, here is a more concrete suggestion (is there a more concise description?)
Limits of continuous functions without the use of calculus or related methods. In particular the evaluation of limits without using L'Hôpital's rule, and the limits of rational functions.
Elementary indicates no calculus allowed. Continuous avoids application of the tag to elementary limits of sums and series