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?

No, never. Yes, always. No, only if

f(x)

is the infinite power tower. No, the limit works for the number of

x

's not mentioned here. No, only if the number of

x

's is finite

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Interesting Power Tower Limit!

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