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Math Help - limit as x -> pi in [[sinx]]

  1. #1
    Junior Member BugzLooney's Avatar
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    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...
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    Quote Originally Posted by BugzLooney View Post
    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...

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

    Tonio
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