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Limit of dirichlet function (from DSP)

  1. Apr 12, 2014 #1
    How is this limit evaluated?

    [tex] \lim_{k->0}\frac{sin(\pi k)}{sin(\frac{\pi k}{N})} [/tex]

    I know that it is N, but I can't figure out how to evaluate it, L'hopitals rule doesn't seem to help.

    I might solve it by the time I get a response, but figured no reason to not ask especially since I couldn't find much about it on Google.

    Solved it, feel like an idiot:

    [tex] \lim_{k->0}\frac{sin(\pi k)}{sin(\frac{\pi k}{N})} [/tex]

    Using L'hopitals rule:

    [tex] \lim_{k->0}N\frac{cos(\pi k)}{cos(\frac{\pi k}{N})} [/tex]

    This is equal to N, since cos(0) = 1.
    Last edited: Apr 12, 2014
  2. jcsd
  3. Apr 19, 2014 #2

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