Suppose that the power series 220:0 0mm\" and 22:0 bum\" converge in some nontrivial interval centered at zero, and consider functions f(:z:) = 22:0 anxn and 9(3) = 230:0 bum\". Prove (without using l'Hopital's Rule!) that if BEE. f(:1:) = HER) g(:1:) = 0, then {E E . M _ . for) 3559c) ' litm