3. (10 Marks) Suppose that the power series _- and" and Enzo box" converge in some non-trivial interval centered at zero, and consider functions f(x) = En anx" and g(x) = En-bna". Prove (without using l'Hopital's Rule!) that if lim f(x) = lim g(x) = 0, f'(0) = g'(0) = 0 and g"(0) = 2023, then f(x) lim lim f'(x) = r+0 g(x) r+0 g'(x)