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Limits Continuity and Differentiability question

2025 · 8 Apr · Shift 2 · Q36

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JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 8 Apr · Shift 2 · Q36

Limits Continuity and Differentiability question

2025 · 8 Apr · Shift 2 · Q36

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Given below are two statements: Statement I:

\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:

\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:

A
Statement I is false but Statement II is true
B
Both Statement I and Statement II are false
C
Both Statement I and Statement II are true
D
Statement I is true but Statement II is false

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