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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If \[f(x)=\left\{ \begin{align}   & \frac{\sin 2x}{5x},\text{when}\,x\ne 0 \\  & \,\,\,\,\,\,\,\,\,\,\,\,k,\text{when }x=0 \\ \end{align} \right.\] is continuous at\[x=0\], then the value of k will be [AI CBSE 1991]

    A)            1

    B)            \[\frac{2}{5}\]

    C)            \[-\frac{2}{5}\]

    D)            None of these

    Correct Answer: B

    Solution :

               \[\underset{x\to 0}{\mathop{\lim }}\,\,f(x)=\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{2\,\,\sin \,2x}{2x\,.\,5}=\frac{2}{5}=k.\]


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