Limit of $\frac{\sqrt{1-\cos x}}x$ using l'Hôpital I'm trying to find
$$\lim_{x\downarrow 0}\frac{\sqrt{1-\cos x}}{x}$$
using l'Hôpital's rule but I seem to be stuck in a loop. I have tried applying l'Hôpital several times but the derivatives always contain the radical and the whole thing ends up being $0\over0$
Is there some way to rewrite $1-\cos x$ or is there something else I'm missing?

Another hint : Multiply the top and the bottom by $\sqrt{1+\cos(x)}$.
