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Question Number 172186 by Mikenice last updated on 23/Jun/22

Commented by kaivan.ahmadi last updated on 24/Jun/22

$$A=x^{x^{x^{....}}}$$$$li\underset{x\to 1}{m}\frac{lnxA}{x^2-1}\stackrel{Hop}{=}li\underset{x\to 1}{m}\frac{\frac{1}{x}A+lnx.A^{\prime }}{2x}=$$$$\frac{1\times 1+0\times A^{\prime }}{2\times 1}=\frac{1}{2}$$

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