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Math Help - e related limit

  1. #1
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    e related limit

    [Math]
    \displaystyle \lim_{x \to + \infty} \left( 1 + \frac {3}{x} \right)^{x/2} =
    [/tex]

    I am simply stumped with this problem.
    All I can say, is there is almost an e in there.

    <br />
(1+\frac{1}{x})^{x}<br />
    This needs to be somehow factored out correct?

    Can someone please guide me through this?
    Much appreciated.
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  2. #2
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    Quote Originally Posted by Vamz View Post
    [Math]
    \displaystyle \lim_{x \to + \infty} \left( 1 + \frac {3}{x} \right)^{x/2} =
    [/tex]

    I am simply stumped with this problem.
    All I can say, is there is almost an e in there.

    <br />
(1+\frac{1}{x})^{x}<br />
    This needs to be somehow factored out correct?

    Can someone please guide me through this?
    Much appreciated.
    let ...

    \displaystyle t = \frac{x}{2}

    x = 2t

    [Math]
    \displaystyle \lim_{t \to + \infty} \left( 1 + \frac {3}{2t} \right)^{t} = e^{\frac{3}{2}}
    [/tex]
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  3. #3
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    Thanks. But I still don't really understand how you got there.
    I think I understand why you set t=x/2, but after that, you've lost me.

    Could you please include the in-between steps?
    Thanks!
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    You already asked about this here

    skeeter just did a change of variable, and \displaystyle \lim_{n \to \infty} \left( 1 + \frac xn \right)^n = e^x
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