(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the first 3 (non-zero) terms of the asymptotic series as x→∞ for ln(e^{x}+1)

2. Relevant equations

ln(1+ε) ~ ε-ε^{2}/2+ε^{3}/3-O(ε^{4}) (x→0)

3. The attempt at a solution

I found

x+ln(1+e^{-x}) (x→∞) = ln(e^{x}+1) (x→∞)ε=ewhich allows me to use the Maclaurin series above (since now the ε→0 as x→∞) yielding^{-x}

x+[e^{-x}-e^{-2x}/2+e^{-3x}/3+O(e^{-4x})]

My question

Is there some expansion I should be using for e^{-x}(x→∞) or some rearrangement of the e^{x}(x→0) that I can use as replacement for e^{-x}to find the next two terms of the series

Thanks

Clay

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# Homework Help: Asymptotic series as x approaches infinity

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