(a) Let $A \subset \mathbb{R}$. What does it mean for a function $f: A \rightarrow \mathbb{R}$ to be uniformly continuous?

(b) Which of the following functions are uniformly continuous? Briefly justify your answers.

(i) $f(x)=x^{2}$ on $\mathbb{R}$.

(ii) $f(x)=\sqrt{x}$ on $[0, \infty)$.

(iii) $f(x)=\cos (1 / x)$ on $[1, \infty)$.