(1) Prove that the Dirichlet function D(x) : R - {0, 1} given by the following rule is not continuous at any point within its domain: if x is rational; D(a) if x is irrational. [10 marks] (2) Prove that f(x) = x2 is uniformly continuous on (0, 1); also prove that f(x) is not uniformly continuous on (0, co). [10 marks]