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 : $$\lim_{x \to 1} \left(x^{\frac{2}{1-x}}\right) = \frac{1}{e^2}$$
In the light of the above statements, choose the correct answer :

A

Statement I is false but Statement II is true

B

Statement I is true but Statement II is false

C

Both Statement I and Statement II are false

D

Both Statement I and Statement II are true