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Limits Continuity and Differentiability question

2025 · 22 Jan · Shift 2 · Q39

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JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 22 Jan · Shift 2 · Q39

Limits Continuity and Differentiability question

2025 · 22 Jan · Shift 2 · Q39

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If

\lim_{x \rightarrow \infty}\left(\left(\frac{\mathrm{e}}{1-\mathrm{e}}\right)\left(\frac{1}{\mathrm{e}}-\frac{x}{1+x}\right)\right)^x=\alpha

, then the value of

\frac{\log _{\mathrm{e}} \alpha}{1+\log _{\mathrm{e}} \alpha}

equals :

A
$e^{-2}$
B
$\mathrm{e}^2$
C
$e$
D
$e^{-1}$

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