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Math Help - How did they get this answer?

  1. #1
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    How did they get this answer?

    What is limx->pi/3 [tan(x)]?

    Answer: sqrt(3)

    Just so it's clear, x is approaching pi/3.

    I really want to understand how they got this answer. Any help is appreciated.
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  2. #2
    Master Of Puppets
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    This is a special value found using the tanget ratio and a special equilateral triangle.

    \displaystyle \lim_{x \to \frac{\pi}{3}}\tan x = \tan\frac{\pi}{3} = \sqrt{3}
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  3. #3
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    Quote Originally Posted by iluvmathbutitshard View Post
    What is limx->pi/3 [tan(x)]?

    Answer: sqrt(3)

    Just so it's clear, x is approaching pi/3.

    I really want to understand how they got this answer. Any help is appreciated.
    from a unit circle value which you as a calculus student should already know ...

    \displaystyle \tan\left(\frac{\pi}{3}\right) = \frac{\sin\left(\frac{\pi}{3}\right)}{\cos\left(\f  rac{\pi}{3}\right)} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}
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