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Finding limits when there is an absolute value in the numerator

  1. Sep 20, 2008 #1
    Ok the problem is:
    lim x->-1 |x+1| / x2-1
    (sorry i don't really know how to type the equation out)

    I think that you have to find the limit as x->-1 from both the left and right sides

    from right:
    so I got lim x->-1 = (x+1)/x2-1 = (x+1)/(x+1)(x-1) = 1/(x-1) =1/-1-1 =-1/2

    How would I go about finding the limit from the left?
  2. jcsd
  3. Sep 20, 2008 #2


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    Welcome to PF!

    Hi katielynn09! Welcome to PF! :smile:

    Just start: "from the left, |x + 1| / x2-1 = -(x + 1) / x2-1 … " :wink:
  4. Sep 20, 2008 #3

    Ok I understand that now. I'm flipped around though. I can't use factoring like I did before because it won't cancel out or substitution because the denominator would still equal 0. What technique would I use to find the limit now?

    can i sort of ignore the negative sign like -1(x+1)/(x+1)(x-1) = -1/-1-1 = 1/2 ?
  5. Sep 21, 2008 #4


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    Hi katielynn09! :smile:

    ooh, you are flipped aren't you?

    yes you can use factoring … the top is just another factor (which happens to be -1) times before …

    ignore the -1, then factor, then put the -1 back again! :smile:
  6. Sep 22, 2008 #5
    thank you :)
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