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!

Homework Help: Calculus Question on Removable Discontinuity

  1. Oct 12, 2014 #1
    I don't entirely understand the question which is why I am posting it here. Anyways, from what the question is asking;we are trying to find the removable discontinuity. This would be plugging in x=0 into both equation and combining them. When this is applied to the first equation, the answer is 0. For the second one, it is 7. So, when the question asks me to combine them, I really don't know what to do with the values. Please Help! I would really appreciate it.
  2. jcsd
  3. Oct 12, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    The first expression doesn't give you 0 at x=0. It's undefined. Follow the suggestion and combine the fractions and simplify!
  4. Oct 14, 2014 #3


    User Avatar
    Science Advisor

    A function, f(x), has a "removable discontinuity" at x= a when [itex]\lim_{x\to a} f(x)[/itex] exists but is NOT equal to f(a). You "remove" the discontinuity by redefining f(a) to be equal to [itex]\lim_{x\to a} f(x)[/itex].

    So for this problem, you need to determine what [tex]\lim_{x\to 0}\frac{4}{x}+ \frac{-x+ 16}{x(x- 4)}[/tex] is and redefine f(0) to be that number. As the problem says, start by getting "common denominators" and adding the two fractions.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted