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Finding removable and jump discontinuities

  1. Oct 15, 2009 #1
    1. The problem statement, all variables and given/known data

    f(x) = -x + b, if x < 2
    = 5, if x = 2
    = -20/(x-b) + 1, if x > 2

    For what value(s) of b does f have a removable discontinuity at 2?
    For what value(s) of b does f have a (finite) jump discontinuity at 2? Write your answer in interval notation.

    3. The attempt at a solution

    I'm completely stumped on the removable discontinuity, because I thought you had to be able to cancel out the bottom?

    And I'm not sure how to find a jump discontinuity.
     
  2. jcsd
  3. Oct 15, 2009 #2

    Dick

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    A removable discontinuity is a value of b where the limit as x->2 from below and the limit as x->2 from above are equal. Your first job is to find those two limits in terms of b. Then equate them. Can you do that?
     
  4. Oct 15, 2009 #3
    Are the limits not -inf and inf?
     
  5. Oct 15, 2009 #4

    Dick

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    No. The limits as x->2! The limit from above is (x>2) is -20/(2-b)+1, isn't it? What's the limit from below?
     
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