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Basic Limit problem?

  1. Oct 25, 2008 #1
    So, I've been mulling over this limit problem for far too long. I feel completely at a loss and refuse to accept my answer of "no limit" or "undefined" regarding the following:

    The limit of (1- (x^.5))/(1+(x^.5)) as x approaches NEGATIVE infinity.

    Someone care to elaborate on what is actually going on here? As I see it, even multiplying by the conjugate, I still end up with an x variable under a radical and so, the square root of any negative number is imaginary. Can such a number "approaching negative infinity" or "x" can also be a positive number, but moving in the negative direction? Being that as it may, I'm trying to keep the answer within the context of real numbers. So, what is the answer?

  2. jcsd
  3. Oct 25, 2008 #2


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    You can't keep x^(0.5) for x negative in the context of the real numbers. Face it. Once you gotten over that, it certainly has a limit in the complex numbers, regardless of branch choice. The answer is -1.
    Last edited: Oct 25, 2008
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