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

Calculus Level 5

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

Evaluate \( \displaystyle \lim_{x\to0^+} (f_{2016} (x) + f_{2017} (x) + f_{2018}(x)) \).

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