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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        \[\underset{x\to \pi /2}{\mathop{\lim }}\,\frac{\sin x}{{{\cos }^{-1}}\left[ \frac{1}{4}(3\sin x-\sin 3x) \right]},\]where\[[.]\] denotes greatest integer function, is

    A)  \[\frac{2}{\pi }\]                                             

    B)  1

    C)  \[\frac{4}{\pi }\]                             

    D)  Does not exist

    Correct Answer: A

    Solution :

                    Given limit is \[L=\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\sin x}{{{\cos }^{-1}}[{{\sin }^{3}}x]}\] Now, when\[x\to \frac{\pi }{2},[{{\sin }^{3}}x]\to 0\]as\[\sin x\to 1\] \[\therefore \]  \[L=\frac{2}{\pi }\]


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