I am being stumped by the following question:
Evaluate the limit by interpreting each as a derivative:
$\lim_{x\,\to\tfrac{\pi}{6}} \frac{\cos(2x) - \frac{1}{2}}{x - \frac{\pi}{6}}$
The only way I can think to solve this is using L'Hopital's rule. I have done that and got the correct answer $-\sqrt{3}$. But, I can not figure out how to do it the was it is described.
Any help would be greatly appreciated.