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Math Help - limits and horz asymptote

  1. #1
    Super Member bigwave's Avatar
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    limits and horz asymptote

    \lim_{x \to -\infty} \frac{x^2}{x^2+x-2}

    and

    \lim_{x \to \infty} \frac{x^2}{x^2+x-2}

    apparently they both approach the horz asymptote of y=1 which must mean they the limit of both is 1

    however what steps are taken from the expression to arrive at this
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  2. #2
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    Divide the top and bottom by x^2. Since limits like 1/x go to zero as x goes to infinity, you should get 1/1 in both cases.
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  3. #3
    Super Member bigwave's Avatar
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    so with

    \frac{1}{1 + \frac{1}{x} - \frac{2}{x^2}}

    by observation as {x \to \pm\infty} it will go to \frac{1}{1} = 1 being the horz asymtope
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