# Limit of dirichlet function (from DSP)

1. Apr 12, 2014

### Jyan

How is this limit evaluated?

$$\lim_{k->0}\frac{sin(\pi k)}{sin(\frac{\pi k}{N})}$$

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:

$$\lim_{k->0}\frac{sin(\pi k)}{sin(\frac{\pi k}{N})}$$

Using L'hopitals rule:

$$\lim_{k->0}N\frac{cos(\pi k)}{cos(\frac{\pi k}{N})}$$

This is equal to N, since cos(0) = 1.

Last edited: Apr 12, 2014
2. Apr 19, 2014

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