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Limit question (from complex analysis)

  1. Apr 9, 2010 #1
    1. The problem statement, all variables and given/known data

    This seems to be just a simple limit problem and I feel like I should know it but I'm just not seeing it.

    I have a continuous function f, and a fixed w

    I want to show that the limit (as h goes to 0) of the absolute value of:

    (1/h)*integral[ f(z)-f(w) ]dz = 0 (the integral is over a contour)

    2. Relevant equations

    I believe the key to the problem is that f is continuous.

    3. The attempt at a solution

    For any a>0 there exists a b>0 such that z within b of w implies f(z) within a of f(w).

    The problem is it seems to me like the 1/h term is going to infinity while the integral term is going to 0, which is indeterminate so I don't know how to get that the limit goes to 0.
  2. jcsd
  3. Apr 9, 2010 #2
    Oh, I have an idea. The contour I'm integrating over is the line connecting w+h to w. So I believe I can use the ML Estimate to show the limit goes to 0...
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