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Continuity and Asymptotes

  1. Sep 19, 2007 #1
    1. The problem statement, all variables and given/known data

    Going over examples of continuity and asymptotes in class, we came across this function:

    f(x) = 6sin(x) / (√X)​

    I know that the numerator is bounded between -1 and 1, and that the denominator increases to infinity. But, my question is...what would be the horizontal asymptote(s) if the equation had been:


    f(x) = tan(x) / (√X)​




    3. The attempt at a solution

    I tried finding the limit both graphically and numerically, and failed to come to any solid conclusion.

    [​IMG]

    Looking at the data table even at intervals in the hundreds of thousandths didn't help.

    [​IMG]

    When I tried analytically I became lost. I know that if the numerator increases faster than the numerator then the horizontal asymptote dne. I also am aware that if the denominator increases faster than the numerator, then the asymptote is 0. But since a tangent function isn't bounded by any limits, like a sinusoid function, I'm not sure how to figure this out.
     
  2. jcsd
  3. Sep 19, 2007 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Do you have any reason to believe it HAS a horizontal asymptote? Unlike sin(x), tan(x) goes to infinity regularly.
     
  4. Sep 19, 2007 #3
    See, I thought at first that because it increases without bound that there would be no horizontal asymptote(s). But for some reason I felt that I missed something, and I am second guessing myself.
     
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