i need to prove that is uniformly continous. now, i thought of a way. i know that
so i acctually need to prove that is bounded ( ). but how do i prove it?
i took a look, and i can see that its limit in infinity (and -infinity) is 0 (is that what you're implying of?) . but as i posted in another post, i don't really know how to solve this limit by myself.
is there any other way except the one with the limit?
See the following very similar post:
Uniform Continuity of $\sqrt{|x|}$ on $\mathbb{R}$
and see "The more sophisticated way" part in
Uniform Continuity of $\sqrt{|x|}$ on $\mathbb{R}$