7. (15 points) (a) Dene What it means for a sequence {f : D > IR} to converge uni formly to the function f : D ) IR. (b) For each n E N, let fn : IR > IR be given by fn(m) 2 502+ $2. in. Prove that the sequence {fn} converges uniformly on IR to the function f : IR > IR given by f(a:) = |LE|. (c) Give an example, with proof, of a domain D and a sequence of func tions which converges pointvvisej but not uniformly on D