Question Number 28093 by tawa tawa last updated on 20/Jan/18
$$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\mathrm{tanx}\right)^{\mathrm{cotx}} \\ $$
Commented by abdo imad last updated on 20/Jan/18
$$={lim}_{{x}\rightarrow\mathrm{0}^{−} } \:\:\:\:\:\:\frac{\mathrm{1}}{\left(\mathrm{1}+{tanx}\right)^{−{cotanx}} }=\:\:\:\frac{\mathrm{1}}{{e}^{−\mathrm{1}} }={e}\:\:\:. \\ $$
Commented by tawa tawa last updated on 21/Jan/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$