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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- Dec 4th 2006, 09:18 AMmyoplex11problem 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). - Dec 4th 2006, 09:49 AMThePerfectHacker
It seems the function,

$\displaystyle h(x)=x \left[ \frac{1}{x} \right]$

Is squeeze between,

$\displaystyle f(x)=1, g(x)=1-x$.

On some open interval except possibly containg the point.

We have,

$\displaystyle 1-x \leq h(x)\leq 1$ for $\displaystyle x>0$

$\displaystyle 1\leq h(x)\leq 1-x$ for $\displaystyle x<0$

And,

$\displaystyle \lim_{x\to 0}1-x=\lim_{x\to 0}1=1$

Now just use the squeeze theorem.

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