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JEE Main & Advanced Sample Paper JEE Main Sample Paper-16

  • question_answer
    The set of values of 'x' for which \[\underset{x\to \infty }{\mathop{\text{L}im}}\,\frac{1}{1+{{\left( \frac{4{{\tan }^{-1}}2x}{\pi } \right)}^{2n}}}\] (where \[n\in N\]) is a non-zero finite quantity, is

    A) \[\left[ \frac{-1}{2},\frac{1}{2} \right]\]                 

    B) \[\left[ 0,\frac{1}{2} \right]\]

    C) \[(-1,1)\]                             

    D) \[\left[ \frac{-1}{2},0 \right]\]

    Correct Answer: A

    Solution :

    \[-1\le \frac{4{{\tan }^{-1}}(2x)}{\pi }\le 1\]or\[\frac{-\pi }{4}\le {{\tan }^{-1}}(2x)\le \frac{\pi }{4}\] \[\Rightarrow \]\[=1\le 2x\le 1\]or\[x\in \left[ \frac{-1}{2},\frac{1}{2} \right]\]


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