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