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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If the function \[f(x)=\left\{ \begin{align}   & \frac{k\cos x}{\pi -2x},\text{when }x\ne \frac{\pi }{2} \\  & 3,\ \ \ \ \ \ \ \ \ \text{when }x=\frac{\pi }{2} \\ \end{align} \right.\] be continuous at \[x=\frac{\pi }{2}\], then k =      

    A)            3

    B)            6

    C)            12

    D)            None of these

    Correct Answer: B

    Solution :

               \[f\,(\pi /2)=3\]. Since \[f(x)\] is continuous at \[x=\pi /2\]                    \[\Rightarrow \,\underset{x\to \pi /2}{\mathop{\lim }}\,\,\left( \frac{k\cos x}{\pi -2x} \right)=f\left( \frac{\pi }{2} \right)\,\,\Rightarrow \,\,\frac{k}{2}=3\,\,\Rightarrow \,\,k=6.\]


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