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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If \[f(x)=\left\{ \begin{align}   & x\sin \frac{1}{x},\,\,x\ne 0 \\  & \,\,\,\,\,\,\,\,\,\,\,\,k,\,\,x=0 \\ \end{align} \right.\]is continuous at \[x=0\], then the value of k is [MP PET 1999; AMU 1999; RPET 2003]

    A)            1

    B)            ?1

    C)            0

    D)            2

    Correct Answer: C

    Solution :

               If function \[f(x)\] is continuous at \[x=0,\] then                    \[f(0)=\underset{x\to 0}{\mathop{\lim }}\,\,f(x)\]                    Given \[f(0)=k\];  \[f(0)=k=\underset{x\to 0}{\mathop{\lim }}\,\,x\,\left( \sin \frac{1}{x} \right)\]            \[f(0)=k=0,\text{  }\left( -1\le \sin \frac{1}{x}\le 1 \right)\];  \[\therefore \,\,\,k=0\]..


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