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Math Help - Need detailed solution

  1. #1
    Nrt
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    Need detailed solution



    I've tried multiplying with ln then L'hospital, but couldnt get to the end.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Nrt View Post


    I've tried multiplying with ln then L'hospital, but couldnt get to the end.
    Note that

    \left(\frac{x-1}{x+1} \right)^{x+1} = \left(\frac{x+1-2}{x+1} \right)^{x+1}=\left(1+\frac{-2}{x+1} \right)^{x+1}

    let u=x+1
    Then as x \to \infty \implies u \to \infty
    so
    \lim_{x \to \infty}\left(\frac{x-1}{x+1} \right)^{x+1}=\lim_{u \to \infty}\left(1+\frac{-2}{u} \right)^{u}=e^{-2}
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