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Question Number 160816 by 0731619 last updated on 07/Dec/21

Commented by mr W last updated on 07/Dec/21

$$f\left(t\right)=t^{t^{t^{...}}}=\frac{W(-\ln t)}{-\ln t}isdefinedonly$$$$fort>0.$$$$witht=\ln x,so{\left(lnx\right)}^{{\left(lnx\right)}^{...}}isonly$$$$definedfor\ln x>0orx>1.$$$$therefore\underset{x\to 0}{\lim }{\left(\ln x\right)}^{{\left(\ln x\right)}^{...}}{doesn}^{\prime }t$$$$exist.$$

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