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Math Help - Vertical and horizontal Asymptotes.

  1. #1
    Member integral's Avatar
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    Vertical and horizontal Asymptotes.

    How would you find the asymptotes of:

    y=\frac{1}{x^2-1}


    So far all my attempts have come up with something dealing with n/0

    (I know how to do it graphically.)
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  2. #2
    Super Member bigwave's Avatar
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    Quote Originally Posted by integral View Post
    How would you find the asymptotes of:

    y=\frac{1}{x^2-1}


    So far all my attempts have come up with something dealing with n/0

    (I know how to do it graphically.)
    when the rational function becomes undefined in this case when x^2-1 becomes 0 then you have a vertical asymptote. so there is vertical asymptotes at \pm1

    also, since f(x)=0 has no solutions, the graph a horizonal asymptote at y=0
    if the degree of the denominator is greater that the degree of the numerator, the x-axis is the horzontal asymptote

    also, what appears sometimes to be asymptotes on a graphing calculator is really just a line going from point to point where there really is a hole in the graph
    Last edited by bigwave; December 29th 2009 at 10:36 PM. Reason: wording
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  3. #3
    Member integral's Avatar
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    Ah, I see.

    So if an equation can not be set to zero then the point were it is undefined, and y=0 (if the denominator is larger than the numerator) are the asymptotes?


    And just so I do not spam with more then one thread.
    Could you please explain How to find points of inflections without using a graph?
    Such as:

    \sqrt[3]{x} were the point of inflection would be 0
    Last edited by integral; December 29th 2009 at 11:34 PM.
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  4. #4
    Super Member bigwave's Avatar
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    basically you find inflection points by taking the f''(x) and setting x = 0

    in this case f''(x) = \left(-\frac{2}{9x^{\frac{5}{3}}}\right)

    and is undefined at x=0
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