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Asymptotic analysis of an algebraic equation

  1. Oct 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Perform an analysis of the algebraic equation y=exp(xy) near x=1/e by substituting y=e+d(x), where d→0 as x→1/e. Solve approximately for d(x) to show that near x=1/e, y(x) has a square root singularity.
    2. Relevant equations

    I don't think there are "relevant equations"

    3. The attempt at a solution

    ln y = xy
    as x-> 1/e, ln (e+d) ~ ln e , that is, ln y ~ 1
    1~x(e+d)
    d~(1/x)-e
    y=e+d
    y~1/x
    So where is "square root singularity"?
     
  2. jcsd
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