Question from the tryout:
This problem just looks scary, doesn’t it? Well, let’s split up the four limits.
First limit, the top left.
l’Hôpital it! Bwahaha.
Now for the top right:
The limit of the floor function approaching from the negative side is the lower number, so this equals .
Indeterminate form (zero over zero), so once again we can use l’Hôpital’s rule on it.
Last limit is the bottom right one.
This one is , so once again we must use l’Hôpital’s rule. This time we apply it twice in succession (because I’m not sure whether or not you can just cancel out the s or not since it’s technically dividing by infinity; ask your local calculus teacher).
Now, we put these solved limits back into the original problem:
Andy? We both fail. XD;