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JEE Main & Advanced Mathematics Functions Question Bank Critical Thinking

  • question_answer
    \[\underset{x\to 1}{\mathop{\lim }}\,(1-x)\tan \left( \frac{\pi x}{2} \right)=\]  [IIT 1978, 84; RPET 1997, 2001;            UPSEAT 2003; Pb. CET 2003]

    A) \[\frac{\pi }{2}\]

    B) \[\pi \]

    C) \[\frac{2}{\pi }\]

    D) 0

    Correct Answer: C

    Solution :

    • \[\underset{x\to 1}{\mathop{\lim }}\,\,(1-x)\tan \,\left( \frac{\pi x}{2} \right)\]. Put \[1-x=y\] as  \[x\to 1,\,\,y\to 0\]                   
    • Thus \[\underset{y\to 0}{\mathop{\lim }}\,y\tan \frac{\pi (1-y)}{2}=\underset{y\to 0}{\mathop{\lim }}\,\frac{2}{\pi }.\] \[\frac{\pi y}{2}\tan \left( \frac{\pi y}{2} \right)=\frac{2}{\pi }\times 1=\frac{2}{\pi }.\]


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