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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If \[f(x)=\left\{ \begin{align}   & \,\,\,\,\,\,\,\,\,\,\,\,x\sin x,\,\text{when }0<x\le \frac{\pi }{2} \\  & \frac{\pi }{2}\sin (\pi +x),\text{when}\frac{\pi }{\text{2}}<x<\pi  \\ \end{align} \right.\], then                    [IIT 1991]

    A)            \[f(x)\]is discontinuous at \[x=\pi /2\]

    B)            \[f(x)\]is continuous at \[x=\pi /2\]

    C)            \[f(x)\]is continuous at \[x=0\]

    D)            None of these

    Correct Answer: A

    Solution :

               \[\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{4x}{(\sqrt{{{x}^{2}}+8x+3}+\sqrt{{{x}^{2}}+4x+3}}\] and \[f\left( \frac{\pi }{2} \right)=\frac{\pi }{2}.\]


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