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Math Help - Limits

  1. #1
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    Limits

    evaluate
    lim x->infinity square root (x^2+9x+1)

    I tried 0, -1, 1, Infinity, and neg. infinity and none were correct.
    help?
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  2. #2
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    My attempt would be,

     \lim_{x \to \infty} \sqrt{x^2+9 x+1} = \sqrt{\infty^2+9\times\infty+1} = \sqrt{\infty} = \infty<br />
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  3. #3
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    Quote Originally Posted by B-lap View Post
    evaluate
    lim x->infinity square root (x^2+9x+1)

    I tried 0, -1, 1, Infinity, and neg. infinity and none were correct.
    help?
    Note that \sqrt{x^2 + 9x + 1} can be expanded using the generalised binomial theorem.

    Alternatively (and less rigorous) note that \sqrt{x^2 + 9x + 1} = \sqrt{\left(x + \frac{9}{2}\right)^2 - \frac{77}{4}} ~ \left|x + \frac{9}{2}\right|.
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