Question Number 169899 by mathlove last updated on 12/May/22
Commented by infinityaction last updated on 12/May/22
$${i}\:{think}\:\:{x}\rightarrow\mathrm{0}^{+\:} {should}\:{be} \\ $$
Commented by mathlove last updated on 12/May/22
$${solve}\:{it}??? \\ $$
Answered by Mathspace last updated on 12/May/22
$${f}\left({x}\right)={x}^{{x}^{{x}} } −{x}^{{x}} \Rightarrow{f}\left({x}\right)={x}^{{e}^{{xlnx}} } −{e}^{{xlnx}} \\ $$$$\Rightarrow{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{f}\left({x}\right)={lim}_{{x}\rightarrow\mathrm{0}} {x}^{\mathrm{1}} −\mathrm{1} \\ $$$$=−\mathrm{1} \\ $$