I literally laughed out loud just now.
My family must think I'm insane.

L'H\^opital Rulez!

Actually, you cannot use L'Hôpitals rule, since the limit for the numerator is not 0. You are thinking of the limit when x -> 0.

It's just zero... Just choose x > 1/eps. Then the function is bounded above by eps and below by -eps.

I'm surprised that guy can even write the Infinity sign without going all starry eyed.

I think this is one I'd better not comment on...

I don't think that guy is a real mathematician, it's most likely the girl that is the mathematician.

isn't it zero? whatever the argument is, the sine function only returns values between -1 and 1, so it could be considered a constant

is this a reference to cyanide and happiness?

I can't help but think of boobies when writing ω (lowercase omega)... :)
I usually write them wider than this font set though... :D

...This joke is way too old to ever be fun. He also looked up and down way too much for the joke to be intransåarent.

Actually, you can use l'Hopital's rule even if you've got a 0/0 instead of an infinity/infinity. Here you can't use it because you use l'Hopital's rule to prove that (sin)'=cos.

And the guy was L'Hospitalized.

hahahahahahhahahaha...L'Hospitalized!!! LOL!!

ha ha ha.....great!

ha ha ha.....great!