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Removable Discontinuities

  1. Nov 2, 2013 #1

    Qube

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    1. The problem statement, all variables and given/known data

    f(x) = ln[(x-x^2)/x]

    Is x = 0 a removable discontinuity?

    2. Relevant equations

    Removable discontinuities are points that can be filled in on a graph to make it continuous.

    3. The attempt at a solution

    Is it? I know that with rational functions, canceling out factors can result in removable discontinuities. For example, the function (x+2)/[(x+2)(x+3)] has a removable discontinuity at x = -2 since the factor (x+2) can be canceled out.

    What about rational functions inside logarithms?
     
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  3. Nov 2, 2013 #2

    Ray Vickson

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    What do you think? If you think the answer is NO, why would you think that? Ditto if you think the answer is YES.
     
  4. Nov 2, 2013 #3

    Simon Bridge

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    @Qube: you appear to have answered your own question without realizing it.
    Probably you need to focus on what it means for a discontinuity to be "removeable".

    ... not quite right is it? If you plotted y=(x+2)/[(x+2)(x+3)] would there be a discontinuity on the graph?
     
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