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Math Help - finding vertical asymptotes of a function

  1. #1
    Red
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    finding vertical asymptotes of a function

    Would like to know where to start on this type of problem, since it's not a regular polynomial that i'm finding the asymptotes for. I'd like to know the process and any helpful tips for this kind of problem. I realize the solution is something along the lines of +-pi +-n(pi) (based on a similar example) but i'd appreciate a dumbed down explanation if possible.

    problem (for simplicity i'll make x = theta):

    Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary nonzero integer if necessary)

    g(x) = (tan 4x)/(3x)
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  2. #2
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    First find points where the function g(x) is not defined.

    In this case they are x=0 and x=Pi/8 + k*(Pi/4)

    Now find:

    \lim_{x \rightarrow 0} \frac{tan(4x)}{3x}

    and \lim_{x \rightarrow \frac{\pi}{8}} \frac{tan(4x)}{3x}

    If the limit goes to infinity then there is vertical asymptote in the corresponding point.

    Regards.
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  3. #3
    Red
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    thanks, looks like the second one is approaching infinity. also wondering though how you find the candidate (other than zero), since i'm not sure how to find out when tan4x/3x = 0 in terms of unit circle. do i use sin/cos?
    Last edited by Red; June 20th 2010 at 09:50 AM.
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  4. #4
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    Yes, the second is approaching infinity so x=Pi/8 + kPi/4 will be all vertical asymptotes.

    Tan(x) is not defined for Pi/2, therefore Tan(4x) will be not defined for Pi/8.

    Regards.
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