Could someone please check my work and let me know if it's correct? I'm not sure my work is completely correct

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 6 > 0 such that If(z) - f(y)| 0 and choose 8 = - 4 . E e 5 - . Then, if a, y E [2, 5] and |x - yl 2 . 2= xy - 2. 2 and since ly - a(e-") |