Question Number 138576 by liberty last updated on 15/Apr/21
$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}+\mathrm{cot}\:\mathrm{2}{x}\right)^{\mathrm{2tan}\:\mathrm{2}{x}} \:=?\: \\ $$
Answered by phanphuoc last updated on 15/Apr/21
$${li}\underset{{u}\left({x}\right)−>\mathrm{0}} {{m}}\left(\mathrm{1}+{u}\left({x}\right)\right)^{\mathrm{1}/{u}\left({x}\right)} ={e} \\ $$$${answer}=\:{e}^{\mathrm{2}} \\ $$