Show limit does not exist

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Homework Statement


Show limit 1/x^2 when x approaches zero does not exist.


Homework Equations





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.
 

Answers and Replies

  • #2
HallsofIvy
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Yes, that is a valid approach.
 
  • #3
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[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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