Find the limit by using the l' Hopital's rule!
\lim_{x\to0}\frac{\cos\!\left(x\right)-1}{2x^2}
So far i got to
\lim_{x\to0}\frac{\-sin\!\left(x}{4x}
What do you do next
But is you call it Bernoulli's rule most (if not all) people won't know what your talking about.
Here's an interesting site.
Calculus I Notes, Section 4-5