Suppose that the power series no anz and nob converge in some non-trivial interval centered at...

 

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Suppose that the power series no anz" and nob" converge in some non-trivial interval centered at zero, and consider functions f(x) = n-on" and g(x) = obna". 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, =0 -0 x-0 then f(x) lim 10 g(x) = f'(x) lim 2-0 g'(x) Suppose that the power series no anz" and nob" converge in some non-trivial interval centered at zero, and consider functions f(x) = n-on" and g(x) = obna". 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, =0 -0 x-0 then f(x) lim 10 g(x) = f'(x) lim 2-0 g'(x)