# limit as x -> pi in [[sinx]]

• Jan 20th 2010, 07:37 PM
BugzLooney
limit as x -> pi in [[sinx]]
Ok so the greatest integer function. What I don't get is why the limit as x->pi of [[sinx]] from the left is 0 but as it approaches pi from the right it is -1? Something I'm missing about the graph because I looked up the graph of sin[x] if that even is the same as [sinx] and it just looks like the limits are both going to 1. Stumped...
• Jan 21st 2010, 12:30 AM
tonio
Quote:

Originally Posted by BugzLooney
Ok so the greatest integer function. What I don't get is why the limit as x->pi of [[sinx]] from the left is 0 but as it approaches pi from the right it is -1? Something I'm missing about the graph because I looked up the graph of sin[x] if that even is the same as [sinx] and it just looks like the limits are both going to 1. Stumped...

$\displaystyle 0<\sin x<1$ for $\displaystyle \frac{\pi}{2}<x<\pi$ and thus $\displaystyle [\sin x]=0$ there, but $\displaystyle -1<\sin x<0$ for $\displaystyle \pi<x<\frac{3\pi}{2}$ and thus $\displaystyle [\sin x]=-1$ there ...

Tonio