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Simple question about limits

  1. Dec 23, 2008 #1
    Obviously [tex] \lim_{x \rightarrow 0} \frac{1}{x^2} = \infty [/tex], but am I correct in saying that the limit as x approaches 0 of [tex] \frac{1}{x^2}[/tex] doesn't exist?

    If it did exist then one of the conditions would be, for values of x sufficiently close to 0, [tex]|x-\infty| = \infty < \delta[/tex] which obviously isn't true for all positive values of delta. Am this correct?
     
    Last edited: Dec 23, 2008
  2. jcsd
  3. Dec 23, 2008 #2
    I think you are correct in saying that the limit does not exist. However,

    [tex]\lim_{x \rightarrow a} f(x) = \infty [/tex] means that for every [tex]N \in \Re[/tex] there exists a number [tex]\delta > 0[/tex] such that, for all x,
    if [tex]0 < |x-a| < \delta[/tex], then [tex]f(x) > N[/tex].
     
    Last edited: Dec 23, 2008
  4. Dec 23, 2008 #3
    I don't know how I made that mistake :rofl:

    Thanks for the reply though :)
     
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