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MCQEasyJEE Main 2023 · 31 January, Shift 2Limits

Mathematics Question from JEE Main 2023 · 31 January, Shift 2

Evaluate the limit: lim⁡x→∞(3x+1+3x−1)6+(3x+1−3x−1)6(x+x2−1)6+(x−x2−1)6⋅x3\lim_{x \to \infty} \frac{\left( \sqrt{3x+1} + \sqrt{3x-1} \right)^6 + \left( \sqrt{3x+1} - \sqrt{3x-1} \right)^6}{\left( x + \sqrt{x^2-1} \right)^6 + \left( x - \sqrt{x^2-1} \right)^6} \cdot x^3

  • A

    is equal to 99

  • B

    is equal to 2727

  • C

    does not exist

  • D

    is equal to 272\frac{27}{2}

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