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JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1+x}-\sqrt{1-x}}{{{\sin }^{-1}}x}=\] [AI CBSE 1989, 90; DSSE 1989]

    A)                 2

    B)                 1

    C)                 ?1

    D)                 None of these

    Correct Answer: B

    Solution :

                       Let \[{{\sin }^{-1}}x=y\,\,\Rightarrow x=\sin y\]            So \[\underset{y\to 0}{\mathop{\lim }}\,\frac{\sqrt{1+\sin y}-\sqrt{1-\sin y}}{y}\]  \[(\because \,\,\,x\to 0\Rightarrow y\to 0)\] \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\log (3+x)-\log (3-x)}{x}=k\]\[\]            =1                                 Aliter : Apply L-Hospital?s rule.


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