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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

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

    A) 3

    B) 6

    C) 12

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[f(\pi /2)=3\]. 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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