$\lim _\limits{x \rightarrow 0} \frac{(1+x)^{y x}-e}{x}$ is

JEE MATHEMATICS MCQ: LIMITS

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\lim \limits_{{x \rightarrow 0}} \frac{(1+x)^{y x}-e}{x}

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Correct option: B

\frac{-e}{2}

Option B (-e/2) is correct because after applying L'Hôpital's rule and simplifying, the limit evaluates to -e/2.

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