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Math Help - Real Analysis Proof

  1. #1
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    Real Analysis Proof

    How would you prove that (1/x^n)-->0 as x-->infinity and (1/x^n)-->0 as x-->-infinity?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by zebra2147 View Post
    How would you prove that (1/x^n)-->0 as x-->infinity and (1/x^n)-->0 as x-->-infinity?
    Show that for all \varepsilon>0 there exists a X_{\varepsilon} such that:for all x>X_{\varepsilon} we have |x^{-n}-0|<\varepsilon

    In this case choose X_{\varepsilon}=\max\left(1,\frac{1}{\varepsilon}\  right), then for x>X_{\varepsilon}:

    |x^{-n}-0|=|x^{-n}|<\frac{1}{x}<\frac{1}{X_{\varepsilon}}\le \varepsilon

    CB
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    Question: I understand what you said besides how you chose ?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by zebra2147 View Post
    Question: I understand what you said besides how you chose ?
    You guess, try a few things, find something that works (there is no unique choice that works, there are plenty of them).

    CB
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