The value of $\mathop {\lim }\limits_{x \to 0} {\left( {\frac{{\sin x}}{x}} \right)^{\frac{{\sin x}}{{x - \sin x}}}}$, is

JEE MATHEMATICS MCQ: LIMITS

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The value of

\lim\limits_{x \to 0} {\left( {\frac{{\sin x}}{x}} \right)^{\frac{{\sin x}}{{x - \sin x}}}}

, is

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Correct option: A

{e^{ - 1}}

Option A (

{e^{ - 1}}

) is correct because using the exponential limit formula and simplifying the expression leads to the correct result.

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