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JEE Main & Advanced Mathematics Differentiation Question Bank Self Evaluation Test - Limits and Derivatives

  • question_answer
    \[\underset{x\to \pi /2}{\mathop{\lim }}\,\frac{\left[ \frac{x}{2} \right]}{ln\,(sin\,x)}\] (where [.] denotes the greatest integer function)

    A) Does not exist

    B) Equals 1

    C) Equals 0

    D) Equals -1

    Correct Answer: C

    Solution :

    [c] \[\because \frac{\pi }{4}<1,\therefore \left[ \frac{\pi }{4} \right]=0\therefore \underset{x\to \pi /2}{\mathop{\lim }}\,\frac{\left[ \frac{x}{2} \right]}{In(sinx)}=0.\]


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