Hey can someone help me solve this? Thanks

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


closed as off-topic by Austin Mohr, Ayman Hourieh, user61527, Stefan Hansen, Michael Hoppe Feb 4 '14 at 6:50

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    $\begingroup$ Enclose it in dollar signs.. $\endgroup$ – J.R. Feb 4 '14 at 0:13
  • $\begingroup$ 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? $\endgroup$ – 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.


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




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


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