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

Hey can someone help me solve this? Thanks

$$\lim_{x \rightarrow 11 \pi/2} \frac{\cos (11 x)}{x - 11 \pi/2}$$

share|cite|improve this question

closed as off-topic by Austin Mohr, Ayman Hourieh, T. Bongers, Stefan Hansen, Michael Hoppe Feb 4 '14 at 6:50

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Austin Mohr, Ayman Hourieh, Community, Stefan Hansen, Michael Hoppe
If this question can be reworded to fit the rules in the help center, please edit the question.

Enclose it in dollar signs.. – Your Ad Here Feb 4 '14 at 0:13
I've edited your post to fix the formatting; please verify that it's correct. Can you please share what you've tried, and explain what you're having trouble with? – user61527 Feb 4 '14 at 0:15

Hint: Let $f(x)=\cos(11x)$. Note that $f(11\pi/2)=0$.

Thus we are looking for $$\lim_{x\to11\pi/2}\frac{f(x)-f(11\pi/2)}{x-11\pi/2}.$$ By definition, this is $f'(11\pi/2)$. Calculate the derivative using the ordinary rules of differentiation.

share|cite|improve this answer

Setting $\displaystyle x-\dfrac{11\pi}2=u$




$$=-11\lim_{u\to0}\left(\frac{\sin11u}{11u}\right)$$ as $\cos\left(\frac\pi2+y\right)=-\sin y$

share|cite|improve this answer

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