Show that the function f(x) = 1/(1 + x^2) for all x in the Reals is uniformly continuous on the Reals.

I'm trying to prove this using the definition of uniform continuity, but I'm having some trouble.

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- Nov 25th 2008, 06:45 AMjkruUniform Continuity
Show that the function f(x) = 1/(1 + x^2) for all x in the Reals is uniformly continuous on the Reals.

I'm trying to prove this using the definition of uniform continuity, but I'm having some trouble. - Nov 25th 2008, 12:56 PMOpalg
Hint: If a function has a bounded derivative then the function is uniformly continuous.

- Nov 25th 2008, 02:15 PMjkru
We're not allowed to use derivatives, unfortunately. Any other ideas on how to attack this problem?

- Nov 26th 2008, 01:19 AMOpalg
In that case, you'll have to use algebra (if that's allowed (Itwasntme) ):

, because . - Nov 26th 2008, 05:51 AMjkru
Haha, yea, I believe it is. Thanks a lot.