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

1. ## 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...

2. 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

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# graph of greatest integer function of sinx

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