Example of Function f:R-R where lim x→0 xf(1/x) ≠ 0

[Trigger]

Please help with the following problem:

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

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

 

[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?

 

[Trigger]

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

 

[dextercioby]

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

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.