1. Not finding help here? Sign up for a free 30min 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!

Limits and functions

  1. Nov 4, 2013 #1
    removable discontinuity

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

    the following function
    f(x)=(4-x)/(16-x^2)


    is discontinuous at???

    i got at -4 but some of my friends say its 4, -4

    how is that possible
     
    Last edited: Nov 4, 2013
  2. jcsd
  3. Nov 4, 2013 #2

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Is the function even defined at ##x = \pm 4##?
     
  4. Nov 4, 2013 #3
    well thats what u have to find

    where is it discontinuous
    i have an exam on this but its not clear yet to me
     
  5. Nov 4, 2013 #4

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Discontinuous doesn't mean the same thing as undefined. Go back to the definition of continuity: can a function be continuous at a point if it is not defined at that point?
     
  6. Nov 4, 2013 #5
    well basically we just have to use the function and find the points where its disconitinuous
    i.e in the graph there is a hole or a jump

    check here
    http://www.dummies.com/how-to/content/how-to-determine-whether-a-function-is-discontinuo.html
     
  7. Nov 4, 2013 #6

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  8. Nov 4, 2013 #7

    0

    but if u factorize the denominator and cancel you will only get -4 as a point of discontinuity

    try it yourself
     
    Last edited: Nov 4, 2013
  9. Nov 4, 2013 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Are you saying that the difficulty is that you do not know what "continuous" means? Didn't It occur to you to look up the definition?

    A function, f, is continuous at x= a if and only if:
    (1) f(a) exists
    (2) [itex]\lim_{x\to a} f(x)[/itex] exists
    (3) [itex]\lim_{x\to a} f(x)= f(a).

    For what values of x is at least one of those NOT true? (Look specifically at (1)!)
     
  10. Nov 4, 2013 #9
    but if u factorise it and cancel the common
    you only get -4 as the point of discontinuity
     
  11. Nov 4, 2013 #10

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Note that
    $$\frac{4-x}{16-x^2}$$
    and
    $$\frac{1}{4+x}$$
    are not the same function. They are equal for ##x \neq 4##, but the first function is undefined (hence discontinuous) at ##x=4## whereas the second is defined and continuous at ##x=4##.

    Therefore the first function has what kind of discontinuity at ##x=4##?
     
  12. Nov 4, 2013 #11

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  13. Nov 4, 2013 #12
    i guess it has a removable one right??
     
  14. Nov 4, 2013 #13

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That's right. After you remove it by canceling the common factor in the numerator and denominator, the result (second function I listed above) is continuous at that point.

    Now what about ##x = -4##? You correctly determined that it is discontinuous there. What kind of discontinuity is it?
     
  15. Nov 4, 2013 #14
    non removable
    but do they both count as discontinuities
     
  16. Nov 4, 2013 #15

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Sure. A removable discontinuity is still a discontinuity. As your link describes it, you can think of it as a "gap" in the graph of the function at ##x = 4##. You can fill the gap by removing the common factor so the denominator will be defined at ##x=4##.
     
  17. Nov 4, 2013 #16
    thanx alot man
    i owe you one
    wish me luck for tomorrows exam
     
  18. Nov 4, 2013 #17

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Absolutely, good luck!
     
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: Limits and functions
  1. Limit of a function (Replies: 2)

  2. Limit of Functions (Replies: 1)

  3. Limit of a function (Replies: 7)

  4. Limit of a function (Replies: 7)

  5. Limit of function (Replies: 6)

Loading...