Millions of years passed still the same unknown \(x\)

Calculus Level 2

\(\large f_n(x) = \Large \underbrace{x^{x^{ x^{x^{\cdot^{\cdot^{\cdot ^x}}}}}}}_{\text{ number of } x \text{'s = } n} \)

What is \( \displaystyle \lim_{x\to0^+} \big(f_{2016} (x) + f_{2017} (x) + f_{2018}(x)\big)? \)

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