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I can't find the limit absolute value function.

  1. Nov 22, 2012 #1

    Vola

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    How find the limit of absolute value function?

    Hi everybody,

    I can't find the limit of (abs(x-2)-2)/x as x-->1.
    I know it's (-1) but I don't see how you get to it.
    If I take (x-2)>0 I get L=-3,(x-2)<0 I get L=-1.
    However according to the graph two sided limit does exist and it's (-1).

    Please help
    Thanks
     
    Last edited: Nov 22, 2012
  2. jcsd
  3. Nov 22, 2012 #2

    Ray Vickson

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    What happens when x is near 1?

    RGV
     
  4. Nov 22, 2012 #3

    Vola

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    is it just a "plug-in" problem?

    (|1-2|-2)/1 => (|-1|-2)/1 => (1-2)/1 =-1?
     
    Last edited: Nov 22, 2012
  5. Nov 22, 2012 #4

    Ray Vickson

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    What is your answer to the question I asked you?

    RGV
     
  6. Nov 22, 2012 #5

    Vola

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    The value of function is negative(?)
     
  7. Nov 22, 2012 #6

    Ray Vickson

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    Let me ask it one last time: if f(x) = (|x-2|-2)/x, what would be the simplified formula for f(x) when x is near 1? Don't guess---calculate!

    RGV
     
  8. Nov 22, 2012 #7

    Vola

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    f(x)=-1
     
  9. Nov 23, 2012 #8

    HallsofIvy

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    Good! For all x less than 2, f(x)= -1 so the limit at any x less than two is -1.

    But you don't "take (x- 2)> 0"! That would be x> 2 and you want the limit at x= 1. You can't "go to 1" if keep x> 2.
     
  10. Nov 23, 2012 #9

    Vola

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    thank you HallsofIvy and Ray
     
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