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Homework Help: What is the difference between Undefined and Nonexistent Limits

  1. Oct 8, 2011 #1
    1. The problem statement, all variables and given/known data
    I am having trouble understanding when limits are undefined and when they do not exist. I googled it and cannot find a good explanation. Can someone please explain this to me?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 8, 2011 #2


    User Avatar
    Homework Helper

    They're interchangeable as far as I know.
  4. Oct 8, 2011 #3


    Staff: Mentor

    Some examples might help.

    Here's one where the limit does not exist.
    [tex]\lim_{x \to 0} \frac{1}{x}[/tex]

    This limit doesn't exist because the left- and right-side limits aren't the same.

    Here's one that's undefined.
    [tex]\lim_{x \to 0} \frac{1}{x^2}[/tex]
    In this limit, the left-and right-side limits are the same, but are undefined, in the sense that infinity is not a number in the real number system.

    That's how I would distinguish between these terms.
  5. Oct 9, 2011 #4
    Thank you. That helped a lot.
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