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

JEE MATHEMATICS MCQ: LIMITS

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The value of

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

, is

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Correct option: A

Option A (1) is correct because after rationalizing and simplifying, the limit evaluates to 1.

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