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Math Help - approaching a limit

  1. #1
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    approaching a limit

    find: lim as x approaches infinity x for the following:

    x(x+1)^1/2*(1-(2x+3)^1/2
    _______________________
    7-6x+4x^2

    I hope this equation is clear. It is a rational equation. I am not sure where to start. I generally know how to evaluate limits at infinity but this one is complicated to me. Any help would be appreciated.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by yoleven View Post
    find: lim as x approaches infinity x for the following:

    x(x+1)^1/2*(1-(2x+3)^1/2
    _______________________
    7-6x+4x^2

    I hope this equation is clear. It is a rational equation. I am not sure where to start. I generally know how to evaluate limits at infinity but this one is complicated to me. Any help would be appreciated.
    \frac{x\sqrt{x+1}(1-\sqrt{2x+3})}{7-6x+4x^2}=\frac{x^2\sqrt{1+1/x}(1/\sqrt{x}-\sqrt{2+3/x})}{x^2(7/x^2-6/x+4)}= \frac{\sqrt{1+1/x}(1/\sqrt{x}-\sqrt{2+3/x})}{7/x^2-6/x+4}

    and now it should be easy.

    RonL
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