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Math Help - problem involving limit and greatest integer function

  1. #1
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    problem involving limit and greatest integer function

    Let f(x) be the greatest integer less than or equal to x.
    compute the lim x->0 xf(1/x).
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  2. #2
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    It seems the function,
    h(x)=x \left[ \frac{1}{x} \right]
    Is squeeze between,
    f(x)=1, g(x)=1-x.
    On some open interval except possibly containg the point.

    We have,
    1-x \leq h(x)\leq 1 for x>0
    1\leq h(x)\leq 1-x for x<0
    And,
    \lim_{x\to 0}1-x=\lim_{x\to 0}1=1
    Now just use the squeeze theorem.

    (You should graph this function. It is the coolest looking thing).
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