# Prove Function is Discontinuous Using Sequences

• Oct 3rd 2007, 02:49 PM
tbyou87
Prove Function is Discontinuous Using Sequences
Hi I have to proove this function is discontinuous at x=0 using the formual definition of continuity:

{ 1 / squareroot(-x) x<0
f(x) = { 0 x = 0
{ 1 / squareroot(x) x > 0

Thanks a lot
• Oct 3rd 2007, 03:07 PM
Plato
Use this sequence: $a_n = \frac{{\left( { - 1} \right)^n }}{{n^2 }}$.
• Oct 3rd 2007, 03:31 PM
tbyou87
How did you find that sequence?
• Oct 3rd 2007, 03:52 PM
Plato
Quote:

Originally Posted by tbyou87
How did you find that sequence?

Thirty-five years of teaching the stuff.
You need not understand how I found it.
You must understand why it works as a counter-example.

Do you see that the sequence converges to zero?
But $\lim _{n \to \infty } f\left( {a_n } \right) = \infty$.