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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    The value of k which makes \[f(x)=\left\{ \begin{align}   & \sin \frac{1}{x},\ x\ne 0 \\  & \,\,\,\,\,\,\,\,k,\,x=0 \\ \end{align} \right.\] continuous at \[x=0\]is                                                                         [MNR 1995]

    A)            8

    B)            1

    C)            ?1

    D)            None of these

    Correct Answer: D

    Solution :

               If \[x\to 0,\] then the value of \[\sin \frac{1}{x}\] passes through [?1, 1] infinitely many ways, therefore limit of the function does not exist at \[x=0.\] Hence there is no value of k for which the function is continuous at \[x=0.\]


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