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Math Help - Question about the type of discontinuity

  1. #1
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    Oct 2009
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    Question about the type of discontinuity

    f(x) = abs (x+3) x<0
    2x + 1 x=0
    (x+2)^2 - 1 x>0

    i found
    lim x->0 = 1
    lim x->0 + - = 3

    so f(x) is not continuous

    but is this removable discontinuity? or jump discontinuity?
    how do i figure it out which is the one?
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  2. #2
    Senior Member
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    Jan 2010
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    If the left-hand and right-hand limits at a point are equal, then it is a removable discontinuity. The idea is that you could "remove" the discontinuity by filling in the hole, leaving you with a smooth curve.

    If they aren't equal, it is a jump discontinuity.
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