# Limit inspiration

Calculus Level pending

Moderator's edit:

Let $$f_1 (x) = x$$ and $$f_{n+1} = x^{f_n (x)}$$ for $$n = 1,2,3,\ldots$$. Compute $$\displaystyle \lim_{x\to0} \lim_{n\to\infty} f_n (x)$$.

$$\lim _{ x\rightarrow 0 }{ { x }^{ { x }^{ { x }^{ { x }^{ { x }^{ x } } } } } }$$ The function is upto infinity.

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