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Math Help - Help with infinite limits

  1. #1
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    Help with infinite limits

    I need a good explanation on how to complete the following problem.

    The limit as x approaches infinity...(64x^2 +x "which is under a square root"
    - 8x)

    Thanks very much
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  2. #2
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    \lim_{x\to\infty}\bigl(\sqrt{64x^2+x}-8x\bigr)

    There is a standard trick for dealing with expressions like this. Make it into a fraction, multiplying top and bottom by the "conjugate" expression (got by changing the – sign to a +):

    \sqrt{64x^2+x}-8x = \frac{\bigl(\sqrt{64x^2+x}-8x\bigr)\bigl(\sqrt{64x^2+x}+8x\bigr)} {\sqrt{64x^2+x}+8x}

    Multiply out the numerator (difference of two squares) and see if you can figure out what then happens as x→∞.
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