Mathematics - Limits Question with Solution | TestHub

Given below are two statements :
Statement I : ${\lim }_{x\to 0}\left(\frac{{\tan }^{-1}x+{\log }_e\sqrt{\frac{1+x}{1-x}}-2x}{x^5}\right)=\frac{2}{5}$
Statement II : ${\lim }_{\mathrm{x}\to 1}\left({\mathrm{x}}^{\frac{2}{1-\mathrm{x}}}\right)=\frac{1}{{\mathrm{e}}^2}$
In the light of the above statements, choose the correct answer from the options given below :