Analysis problem

1. Dec 7, 2004

Trigger

Find an example of a finction f:R-R where

lim x tends towards zero of xf(1/x) is not zero

2. Dec 7, 2004

Galileo

It would obviously be the case when f(1/x) can cancel the x, so that the limit is independent of x.
What would f(x) have to be, if f(1/x) is to be proportional to 1/x?

3. Dec 7, 2004

Trigger

Would f(x) have to be -x squared if f(1/x) is to be proportional to 1/x

4. Dec 7, 2004

dextercioby

Hint:Relabel 1/x with "lambda",get the old function f(1/x) in terms of "lambda" and then simply rename "lambda" as being x.U'll get your answer.