Could someone please help me with part two of this problem and check my work for part three. I think part one is OK

Suppose f: D-+ IR is continuous on a compact sot D. Then of is uniformly continuous on D. Therem 5.4.9 A function f: (ab)-R is uniformly continuous on (a, 6 ) iff it can be extended To a function of That is continuous on [a, 6]. Please state all definitions and theorems that you will need: es 4 . E Definition 5.4.1 = E Let f : D - R . We say that f is uniformly continuous on D if for every & > 0 there exists a Thus, f is uniformly continuous on [2, 5] by definition 5.4.1 8 > 0 such that If(x) - f(y) | 0 , letx = ... and y = ... . Then, if z, y E (0, 2) and 1. f (x) = - |x - yl = ... 0 and choose 8 = 4 e5 . Then, if a, y E [2, 5] and |ac - yl 1 If (z) - f(y)1 = ey 3. f(2) = =2+ 32 - 5 on [0, 4). yet - xet cy Let & > 0 and choose o = 7 . Then, if x, y E [0, 4] and |x - yl