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Math Help - limits problem

  1. #1
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    limits problem

    <br />
\lim_{x \to \pi/3}\frac{\tan^3(x) -3\tan(x)}{\cos(x+\pi/6)}<br />

    help please
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  2. #2
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    Take the derievative of the top and bottom.

    In other words Apply L' Hospitals Rule, it becomes and elementary problem.

    <br /> <br />
3\lim_{x \to \pi/3}\frac{\tan^{2}(x)sec^{2} -3\sec^{2}x}{\-sin(x+\pi/6)}<br />

    Evaluate it and ta-da.


    The answer is negative 12 i believe but don't trust me, do it yourselve.
    Last edited by Banned for attempted hacking; May 11th 2009 at 04:47 PM.
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  3. #3
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    \lim_{x\to \frac{\pi}{3}}\frac{tan^{3}(x)-3tan(x)}{cos(x+\frac{\pi}{6})}

    Have you learned L'Hopital's rule yet?.

    Differentiate top and bottom:

    \lim_{x\to \frac{\pi}{3}}\frac{-3(tan^{4}(x)-1)}{sin(x+\frac{\pi}{6})}

    Now, just plug in x=Pi/3 and you got it. You should get -24
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  4. #4
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    -24 is correct. told you not to trust me.
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