The value of $\mathop {\lim }\limits_{x \to \infty } {\left( {\frac{{1 + 3x}}{{2 + 3x}}} \right)^{\frac{{1 - \sqrt x }}{{1 + x}}}}$, is

JEE MATHEMATICS MCQ: LIMITS

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The value of

\lim\limits_{x \to \infty } {\left( {\frac{{1 + 3x}}{{2 + 3x}}} \right)^{\frac{{1 - \sqrt x }}{{1 + x}}}}

, is

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Correct option: D

Option D (1) is correct because, as x approaches infinity, the base approaches 1 and the exponent approaches 0, resulting in a limit of 1.

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