Let {a_{n}},{b_{n}}, {c_{n}} be three sequence converges to a, b, c respectively.

(a) Let B > 0 be a real number. Let f_{n}(x) = a_{n}+ b_{n}x + c_{n}x^{2}. Show that {f_{n}} converges uniformly to f(x) = a + bx + cx^{2}on [-B,B].

(b) Prove or disprove that {f_{n}} converges uniformly to f(x) on R.