Homework Help: Show limit does not exist

1. Nov 22, 2011

Hwng10

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. Nov 22, 2011

HallsofIvy

Yes, that is a valid approach.

3. Nov 22, 2011

Staff: Mentor

$$\lim_{x \to 0}\frac{1}{x^2} = \infty$$

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.