Thread: 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).

It seems the function,

Is squeeze between,
.
On some open interval except possibly containg the point.

We have,
for
for
And,

Now just use the squeeze theorem.

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