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Limit question limit (x->0) 1/|x|

  1. Aug 29, 2010 #1
    limit (x->0) 1/|x|
     
  2. jcsd
  3. Aug 29, 2010 #2
    the limit doesn't exist.
    lim (x-> o+) = + ∞
    lim (x-> o-) = - ∞

    so limit of the function at the point zero is not existent by definition.
     
  4. Aug 29, 2010 #3

    Mentallic

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    Not true. The function is 1/|x| not 1/x
     
  5. Aug 29, 2010 #4
    aah yea you're right. didn't notice the abs function there. anyway, when x approaches zero from left (and right) the function approaches +∞. so the limit is +∞.

    that means for all positive deltas and M's if |x - 0| < delta, then f(x) > M. for any large M you like. intuitively you can say: the larger you want M to be, the smaller you need to take delta.
     
    Last edited: Aug 30, 2010
  6. Aug 30, 2010 #5

    HallsofIvy

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    Which still means that there is no limit. Saying "[itex]\lim f(x)= \infty[/itex]" is just a way of saying that the limit does not exist for a particular reason.
     
  7. Aug 30, 2010 #6
    well, I think if we're working on extended real number line then it doesn't hurt to say the limit of the function is +∞ because +∞ ∈ R*. and plus the epsilon, delta definition works fine with this example. correct me if i'm wrong.
     
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