JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{3+x}-\sqrt{3-x}}{x}=\] [MP PET 1987]

    A)                 ?1

    B)                 0

    C)                 \[\sqrt{3}\]

    D)                 \[\frac{1}{\sqrt{3}}\]

    Correct Answer: D

    Solution :

                       \[\underset{x\to 0}{\mathop{\lim }}\,\frac{2x}{x\,(\sqrt{3+x}+\sqrt{3-x})}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}}.\]                                 Aliter : Apply L-Hospital?s rule two times.


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