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Math Help - limit at infinity of a difference of squares

  1. #1
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    limit at infinity of a difference of squares

    How does one tackle a question like

    limit as x -> + or - inf of [sqrt(f(x)) - sqrt(g(x))]

    f(x) and g(x) are both quadratics of the form ax^2 + bx + c

    I multiplied by the conjugate but then I get square roots in the denominator going to infinity.

    here is the question:

    limit at infinity of a difference of squares-screen-shot-2014-03-04-5.48.58-pm.png

    after multiplying by the conjugate I get

    limit at infinity of a difference of squares-expression2.gif

    Then i divide both top and bottom by x to get 11/4

    if I take the limit going to negative infinity will the answer still be 11/4?
    Attached Thumbnails Attached Thumbnails limit at infinity of a difference of squares-expression.gif  
    Last edited by kingsolomonsgrave; March 4th 2014 at 02:25 PM.
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  2. #2
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    Re: limit at infinity of a difference of squares

    Yes it will be.
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