This is the most common type of L'Hopital's Rule problem, taking limits of indeterminate fractions. You need derivatives for this, but once you see it, you'll be kicking yourself that your teacher made you do limits the hard way for so long!
L'Hopital's With Indeterminate Exponents
This is a very rare, and very difficult, type of limit problem that almost no calculus teachers make you do. But if you've got a tough teacher, this could be for you. In this video we take the limit of xx and (sinX)x, which might not look that bad, but you can't take the derivative of them any other way.
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)