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Homework Help: Show limit does not exist

  1. Nov 22, 2011 #1
    1. The problem statement, all variables and given/known data
    Show limit 1/x^2 when x approaches zero does not exist.

    2. Relevant equations

    3. The attempt at a solution
    What I do is suppose the limit exists,say L.Then I show that for all real number L, the limit does not approaches L. In this case, I separate L into different cases. Can anyone help me to check is this a valid prove.
  2. jcsd
  3. Nov 22, 2011 #2


    User Avatar
    Science Advisor

    Yes, that is a valid approach.
  4. Nov 22, 2011 #3


    Staff: Mentor

    [tex]\lim_{x \to 0}\frac{1}{x^2} = \infty[/tex]

    Since ∞ is not a real number the limit above is said not to exist. This limit means that for any large, positive number M, there is some interval around 0 such that if x is in that interval, 1/x2 > M.
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