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Math Help - limit as x approaches negative infinity

  1. #1
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    limit as x approaches negative infinity

    as x approaches negative infinity, what value does this function approach ?
    limit square root (X^2+X) + X

    i manipulated it to take out absolute (x) from the square root

    so, limit absolute value (x) square root (1+1/x) +x

    now, i get infinity - infinity.
    I do not know where to go from this point.

    Thanks
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  2. #2
    MHF Contributor matheagle's Avatar
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    I get -.5, but you need to be careful with the negative sign.
    Moving an x through a square root is not x, but |x|=-x in this case.

    let w=-x and then multiply top and bottom by the conjugate and see what you get.
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  3. #3
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    You mean, I take it, \lim_{x\to -\infty} \sqrt{x^2+ x}+ x.

    Yes, matheagle is right. Multiplying "numerator and denominator" by \sqrt{x^2+ x}- x give a limit of -\frac{1}{2}= -0.5.
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