Question

Prove that the function x^3 is not uniformly continuous in R.

Answer 1

this is fairly easy to do but rather a pain to write
i think a google search will probably clear it up, but the main idea is that \(x^3-y^3=(x-y)(x^2+xy+y^2)\) so while you can choose \(x-y\) as small as you like, the second term, the one with squares, can be made large

Answer 2

yes, look at d here

Answer 3

Thanks! You are a life saver!