- #1
Jyan
- 36
- 2
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.
[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.
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