1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Removable Discontinuities

  1. Nov 2, 2013 #1


    User Avatar
    Gold Member

    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?
  2. jcsd
  3. Nov 2, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    @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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Removable Discontinuities