- #1
rg2004
- 22
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Homework Statement
Find the first 3 (non-zero) terms of the asymptotic series as x→∞ for ln(ex+1)
Homework Equations
ln(1+ε) ~ ε-ε2/2+ε3/3-O(ε4) (x→0)
The Attempt at a Solution
I found
x+ln(1+e-x) (x→∞) = ln(ex+1) (x→∞)
ε=e-x
which allows me to use the Maclaurin series above (since now the ε→0 as x→∞) yielding 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 ex (x→0) that I can use as replacement for e-x to find the next two terms of the series
Thanks
Clay