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Piece-Wise Function Continuity

  1. Sep 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold.

    f(x)= {x^3 if x < or = -2
    {2 if x > -2

    2. Relevant equations
    The conditions are that a function is said to be continuous at x=c if the following conditions hold:
    1 f(c) exists
    2 lim as x approaches c f(x) exists
    3 lim as x approaches c f(x) = f(c)

    3. The attempt at a solution
    My professor has not explained this and has assigned it...no clue what to do!
  2. jcsd
  3. Sep 7, 2011 #2


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    You will have to calculate the limit in each point and see whether the left and right sided limits are equal.
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