Thread: 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.

Originally Posted by myoplex11

multiply by x:
1-x =< x[1/x] =< 1

Almost.
You just need to consider 2 cases when 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?)