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Math Help - limit-trigo

  1. #1
    Super Member dhiab's Avatar
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    limit-trigo

    calculate this limit ( no hospital ) :

     <br />
\lim_{x\rightarrow \frac{\pi }{3}}(\frac{2cos(x)+1}{x-\frac{\pi }{3}})<br />
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dhiab View Post
    calculate this limit ( no hospital ) :

     <br />
\lim_{x\rightarrow \frac{\pi }{3}}(\frac{2cos(x)+1}{x-\frac{\pi }{3}})<br />
    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:

     <br />
\displaystyle \lim_{x\to \frac{\pi }{3}}\left(\frac{2\cos(x)-1}{x-\frac{\pi }{3}}\right)<br />

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


    CB
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