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!

If you try to use L'Hospital's rule to evaluate
$$ \lim_{x\to\infty} \frac{2x}{x+\sin x} $$
you end up with
$$ \lim_{x\to\infty} \frac{2}{1+\cos x} $$
which spectacularly fails to converge. But the original limit does exist (it is $2$).
