Are there any limit questions which are easier to solve using methods other than l'Hopital's Rule? Are there any limit questions which are easier to solve using methods other than l'Hopital's Rule? It seems like for every limit that results in an indeterminate form, you may as well use lHopital's Rule rather than any of the methods that are taught prior to the rule, such as factoring, rationalizing, trig limits, etc.
EDIT: These are great answers, thanks!

It was suggested in the comment but never given explicit mention in an answer, so here is a simple limit that cannot be computed by L'Hopital rule simply because it is not differentiable.

$\lim_{t\to 0} \dfrac{1}{t \lfloor \frac{1}{t} \rfloor} = 1$.

For more details on a more intuitive technique to handle everything that L'Hopital's rule can and more, see this related post on MathEducators SE, where usually an asymptotic form of the Taylor theorem (I give a proof here) gives far more information than L'Hopital's rule.
