Limit Evaluation Statements (Jee Mains)

Evaluation of Limits

Medium

Limit Evaluation Statements

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

SELECT ONE OPTION

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