problem involving limit and greatest integer function

• December 4th 2006, 09:18 AM
myoplex11
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).
• December 4th 2006, 09:49 AM
ThePerfectHacker
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).