Suppose that the power series P n=0 anxn and P n=0 bnxn converge in some non-trivial interval centered at zero, and consider functions f(x) = P n=0 anxn and g(x) = P n=0 bnxn. Prove (without using l'Hopital's Rule!) that if limx0 f(x) = limx0 g(x) = 0, f'(0) = g'(0) = 0 and g"(0) = 2023, then limx0 f(x)/g(x) = limx0 f'(x)/g'(x) .