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Math Help - limits indeterminate form

  1. #1
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    limits indeterminate form

     <br />
\displaystyle\lim_{x\to\infty}<br />

    (1-1/x)^5x

    Can someone please help with this one i dont even know where to start?
    thank you
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  2. #2
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    Hello, cowboys111!

    I believe you are expected to know that: . \lim_{u\to\infty}\left(1 + \frac{a}{u}\right)^u \;=\;e^a


     \displaystyle\lim_{x\to\infty}\left(1-\frac{1}{x}\right)^{5x}

    We have: . \lim_{x\to\infty}\left[\left(1 + \frac{\text{-}1}{x}\right)^x\right]^5 \;=\;\left[\lim_{x\to\infty}\left(1 + \frac{\text{-}1}{x}\right)^x\right]^5\;=\;\left[e^{-x}\right]^5 \;=\;e^{-5x}<br />

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  3. #3
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    I sure that it is a typo.
    The limit is e^{-5}.
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  4. #4
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    ok thats easy enough i just didnt know that
    thanks for the help
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