Which Functions Satisfy These Limit Conditions?

[dey]

Find a function (or several or all) f(x) which satisfied all these three conditions:
(1) lim [x→∞] f(x)/aˣ = 0 if a ≥ e (2) f(x)/aˣ → ∞ when x→∞ if 0 < a < e
(3) lim [x→∞] f(x)1/x = e.

 

[dey]

try it!