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Complex limit

  1. Feb 12, 2008 #1
    [SOLVED] complex limit

    1. The problem statement, all variables and given/known data
    Evaluate the complex limit if it exists:

    [tex]\lim_{z \to 1} \frac{\log{z}}{z-1}[/tex]

    where log denotes the principal branch of the logarithm.

    2. Relevant equations

    3. The attempt at a solution
    I am pretty sure it exists and equals 1, because that is what it equals when I approach with specific sequences. But how can I prove that?
  2. jcsd
  3. Feb 12, 2008 #2

    Gib Z

    User Avatar
    Homework Helper

    [tex]\lim_{z \to 1} \frac{\log{z}}{z-1} = \lim_{z\to 0} \frac{\log (1+z)}{z}[/tex].

    Are you allowed to use the property that the series for that log term converges to that log term iff |z| < 1?
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