Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Attached Files:

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Limit dirichlet function Date
B Question about a limit definition Feb 27, 2018
I Looking for additional material about limits and distributions Feb 17, 2018
I A problematic limit to prove Jan 26, 2018
B Proof of a limit rule Dec 19, 2017
Dirichlet's formula proof Dec 21, 2010