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Math Help - Limits Problem

  1. #1
    Super Member craig's Avatar
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    Limits Problem

    Show that for any k, \lim_{x\to\infty}\frac{x^{k}}{e^{x}}\to0.

    I'm thinking that this has something to do with l'Hopital's Rule, showing that x^{k} > e^{x}, not sure where to start though?

    Thank in advance
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  2. #2
    MHF Contributor chisigma's Avatar
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    Applying k times L'Hopital's Rule You obtain...

    \lim_{x \rightarrow \infty} \frac{x^{k}}{e^{x}} = \lim_{x \rightarrow \infty} \frac{k!}{e^{x}} = 0

    Kind regards

    \chi \sigma
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