# limit-trigo

• October 12th 2010, 08:14 PM
dhiab
limit-trigo
calculate this limit ( no hospital ) :

$
\lim_{x\rightarrow \frac{\pi }{3}}(\frac{2cos(x)+1}{x-\frac{\pi }{3}})
$
• October 12th 2010, 08:40 PM
CaptainBlack
Quote:

Originally Posted by dhiab
calculate this limit ( no hospital ) :

$
\lim_{x\rightarrow \frac{\pi }{3}}(\frac{2cos(x)+1}{x-\frac{\pi }{3}})
$

Because:

$\displaystyle \lim_{x\to \frac{\pi }{3}}\left[2\cos(x)+1\right] \ne 0$

(since $\cos(\pi/3)=1/2$ ), The limit does not exist.

Or are you asking for:

$
\displaystyle \lim_{x\to \frac{\pi }{3}}\left(\frac{2\cos(x)-1}{x-\frac{\pi }{3}}\right)
$

(Expanding the numerator as a Taylor series about $\pi/3$ this can be seen to be $-\sqrt{3}$ )

CB