3. Suppose that fn -+ f and gn -+ g, as n -+ 00, uniformly on some set E S;;; R.

(a) Prove that fn + gn -+ f + 9 and afn -+ af, as n -+ 00, uniformly on E for allaER.

(b) Prove that f ngn -+ f 9 pointwise on E.

(c) Prove that if f and 9 are bounded on E, then fngn -+ fg uniformly on E.

(d) show that

(c) may be false when 9 is unbounded.