I'm confused:

Why is the limit(as x -> 0) sin(x)/(x-sin(x)) = infinity?

I have done this 10 times now, and I get that it equals -1.

We have an indeterminant form when we plug 0 in (0/0). Thus, I can use l'hopitals rule.

Then:

cos(x)/(1-cos(x)) = 1/0...doesn't work, so do l'hopitals again.

-sin(x)/sin(x) = 0/0; use l'hopitals again

-cos(x)/cos(x) = -1/1 = -1

So, how does it equal infinity?