So I was given this question on a worksheet and I'm pretty sure I have it but the solution seems a little too simple. Can someone let me know if I'm missing something?
"Why do you know, without any computation, that $f(x) = \sqrt x$ is uniformly continuous on the interval $[0.01,100]$. Then, find a $\delta$ that corresponds to an arbitrary choice of $\epsilon \gt 0$ that satisfies the definition of uniform continuity."
I think the answer is that since $[0.01,100]$ is a compact interval it is then uniformly continuous. Then for part 2 of the question I'm thinking that $\delta = \epsilon$ which seems a little trivial. Can someone help me confirm this?