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Math Help - limit problem

  1. #1
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    limit problem

    Let f(x) be the greatest integer less than or equal to x.
    Compute lim x->0 xf(1/x). Is the following solution correct.

    f(1/x)=[1/x]
    lim x->0 xf(1/x) = lim x->0 x[x]

    Note that:
    (1/x)-1 =< [1/x] =< 1/x
    multiply by x:
    1-x =< x[1/x] =< 1

    since the limit x->0 (1-x)=1 and the limit x->0 1= 1 then
    by squeeze theorem the lim x->0 x[1/x] = 1.
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  2. #2
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    Quote Originally Posted by myoplex11 View Post
    multiply by x:
    1-x =< x[1/x] =< 1
    Almost.
    You just need to consider 2 cases when x positive and negative. It will change the signs!

    (What are you doing? I already posted a solution to this in the other thread. Or are you trying to derive what I said mathematically?)
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