JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\cos \frac{1}{x}\] [UPSEAT 2002]

    A)                 Is continuous at \[x=0\]

    B)                 Is differentiable at \[(3,\,\,1)\]

    C)                 Does not exist

    D)                 None of these

    Correct Answer: C

    Solution :

                       \[\underset{x\to 0}{\mathop{\lim }}\,\,\cos \frac{1}{x}\] oscillates between \[-1\] and 1.                 \ Limit doesn?t exist.


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