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Does there exist a continuous function which outgrows polynomial growth, but not exponential growth?
I.e. does a there exist a continuous function f such that [tex]\frac{x^n}{f(x)} \to 0[/tex] and [tex]\frac{f(x)}{a^x} \to 0[/tex] for all positive real n and a?
I.e. does a there exist a continuous function f such that [tex]\frac{x^n}{f(x)} \to 0[/tex] and [tex]\frac{f(x)}{a^x} \to 0[/tex] for all positive real n and a?