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Limits question

  1. Sep 27, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the limit of x^2/(x-1) as x goes to 1 from the left.

    2. Relevant equations

    3. The attempt at a solution
    It doesn't seem I can factor anything, but could I assume that since the numerator is a constant and the denomination is going to be negative because it's <1 then it's going to negative infinity? Is there anyway to show this algebraically? Thanks.
  2. jcsd
  3. Sep 27, 2010 #2
    You are correct.

    [tex] \frac{x^2}{1-x} = \frac{x^2 -1}{1-x} + \frac{1}{1-x}[/tex]

    The limit as x-> [tex]1^{-}[/tex] of [tex]\frac{x^2 -1}{1-x} [/tex] is 2.
    [tex]\frac{1}{1-x}[/tex] one does not exist.
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