Question Number 142308 by qaz last updated on 29/May/21
![lim_(x→0) ((lnlnln[x+(1+x)^(((1+x)^(1/x) )/x) ]+x(1−(1/e^(e+1) )))/x^2 )=?](https://www.tinkutara.com/question/Q142308.png)
$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{lnlnln}\left[\mathrm{x}+\left(\mathrm{1}+\mathrm{x}\right)^{\frac{\left(\mathrm{1}+\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} }{\mathrm{x}}} \right]+\mathrm{x}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{e}^{\mathrm{e}+\mathrm{1}} }\right)}{\mathrm{x}^{\mathrm{2}} }=? \\ $$