Interesting Power Tower Limit!

Calculus Level 4

\[\lim_{x\to 0^-} f(x) = \lim_{x\to 0^+} f(x)\]

Consider the power tower function \(f(x)\), where there are many \(x\)'s. Is the above limit true for all numbers of \(x\)'s, including infinitely many \(x\)'s?

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