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Math Help - limits help

  1. #1
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    limits help

    I am trying to solve these limits, but have some questions:

    1) lim x -> -infinity (3x / (1 + (2/x)) = -infinity. then it says DNE. why?

    2) limit x -> -infinity [x/(sqrt(x^2 -2x))] = ? would I divide by x on the top and bottom here?
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  2. #2
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    Re: limits help

    Quote Originally Posted by droidus View Post
    1) lim x -> -infinity (3x / (1 + (2/x)) = -infinity. then it says DNE. why?
    If the limit is infinite, then the limit does not exist.

    Quote Originally Posted by droidus View Post
    2) limit x -> -infinity [x/(sqrt(x^2 -2x))] = ? would I divide by x on the top and bottom here?
    Yes, that would work. Or

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

    =\lim_{x\to\infty}\frac x{\sqrt{x^2\left(1-2/x\right)}}

    =\lim_{x\to\infty}\frac x{x\sqrt{1-2/x}}

    =\lim_{x\to\infty}\frac 1{\sqrt{1-2/x}}

    =\frac 1{\sqrt{1-0}} = 1
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