Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
up vote 3 down vote accepted

Hint: Write down the definition of the derivative of $f(x)=\cos 2x$ at $\frac{\pi}6$

share|cite|improve this answer
I sure did not realize how simple the question actually was. Thank you – Richard Dec 24 '12 at 18:29

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.