I know this work is correct but could someone please answer the three questions I have in black ink

Please state all definitions and theorems that you will need: Definition 5.4.1 Let f: D - R . We say that f is uniformly continuous on D if for every & > 0 there exists a 8 > 0 such that If (x) - f(y)| z. (b) For each x > 0 and for each y E R , there exists an n E N such that na > y . (c) For each > > 0 , there exists an n E N such that 0 0 and choose S = In & - 5 . Then, if x, y E [2, 5] and (x - y|