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Asymptotic expansions

  1. Sep 16, 2008 #1
    Can anyone tell me how to find a two-term asymptotic expansion for the two real roots of xe-x=epsilon as epsilon --> 0

    Thanks,
    A.Haywood
     
  2. jcsd
  3. Sep 17, 2008 #2
    dear Haywood
    I don't know what kind of asypmtotic expasion you are looking for, so a short hint on how to solve the equation approximatly must suffice.
    For the root near 0 substitute the left hand side with a taylor polynomial.
    For the other root take logarithms on both sides.
     
  4. Sep 21, 2008 #3
    That works!!! I was especially looking for how to find that second root, so grateful that you mentioned using ln :-)
    Thank you, Dalle!
     
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