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Math Help - lim (1-(3/x))^x

  1. #1
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    lim (1-(3/x))^x

    Please help me how to resolve this calculus...

    lim (1-(3/x))^x
    x to +infinity
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  2. #2
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    Quote Originally Posted by maiya View Post
    Please help me how to resolve this calculus...

    lim (1-(3/x))^x
    x to +infinity
    1. You are supposed to know that \lim_{n \to +\infty}\left(1 - \frac1n\right)^n = e

    2. Use the substitution \frac3x =\frac1n~\implies~x=3n

    3. Your limit becomes now:

    \lim_{n \to +\infty}\left(1-\frac1n \right)^{3n} =\left( \lim_{n \to +\infty}\left(1-\frac1n \right)^{n}\right)^3 = e^3
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    Super Member Random Variable's Avatar
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  4. #4
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    Quote Originally Posted by earboth View Post
    1. You are supposed to know that \lim_{n \to +\infty}\left(1 - \frac1n\right)^n = e

    2. Use the substitution \frac3x =\frac1n~\implies~x=3n

    3. Your limit becomes now:

    \lim_{n \to +\infty}\left(1-\frac1n \right)^{3n} =\left( \lim_{n \to +\infty}\left(1-\frac1n \right)^{n}\right)^3 = e^3
    tqvm..
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  5. #5
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    Quote Originally Posted by Random Variable View Post
    tqvm..
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