2. Suppose that In 2 0 is a sequence of integrable functions that satisfies lim In (x) d.x = 0. n-too Ja Show that if f : [a, b] -> R is integrable on [a, b], then lim f(x)gn(x)dx = 0.3. Suppose that f is a nonnegative continuous function on a closed nondegenerate interval [a, b]. Show that fo f(x) dx = 0 if and only if f(x) = 0 for all r E [a, b]