If lim_(x → ∞) ( e/(1 - e) ( 1/e - x/(1 + x)))^x = α, then the va… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 22 January, Shift 2Limits

If $\lim_{x \to \infty} \left( \frac{e}{1 - e} \left( \frac{1}{e} - \frac{x}{1 + x} \right) \right)^x = \alpha,$ then the value of $\frac{\log_e \alpha}{1 + \log_e \alpha}$ equals:

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

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