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Thread: limits to infinity

  1. November 29th 2009, 02:58 AM #1
    alexandrabel90
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    limits to infinity

    how do you find
    lim of (1 + 2/x)^x as x tends to infinity?
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  2. November 29th 2009, 03:16 AM #2
    tonio
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    Quote Originally Posted by alexandrabel90 View Post
    how do you find
    lim of (1 + 2/x)^x as x tends to infinity?

    If you already know that \lim_{x\to\infty}\left(1+\frac{1}{f(x)}\right)^{f( x)}=e\,,\mbox { for any function }f(x)\mbox{ s.t. } f(x)\xrightarrow [x\to\infty] {}\infty \mbox{ whenever } x\rightarrow \infty ,then:

    \lim_{x\to\infty}\left(1+\frac{2}{x}\right)^x=\lim _{x\to\infty}\left[\left(1+\frac{1}{x\slash 2}\right)^{x\slash2}\right]^2=e^2

    Tonio
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