Find the limit of xsin(pi*x) at infinity

1. Feb 23, 2005

allergic

Since the function f(x)=xsin[(pi)x] oscillates, shouldnt the limit as x -> infinity not exist? i was told that it is positive infinity.

2. Feb 23, 2005

arildno

If your function really is $$f(x)=x\sin(\pi{x})$$ , then you're right.
(That is, a limit doesn't exist)

Last edited: Feb 23, 2005
3. Feb 23, 2005

dextercioby

Note,that "pi" in the argument is totally unimportant.A certain rescaling would eliminate it...

Daniel.

4. Feb 23, 2005

arildno

Unless, of course, x is supposed to be an integer variable; in which case a limit does exist..

5. Feb 23, 2005

dextercioby

Of course,Arildno,mathematicians thought of it and decided to use the "n" (middle Latin alphabet letters,in general) for the INTEGER/natural numbers.Just the same way as "x" stands for reals and "z" for complex...

Daniel.

6. Feb 23, 2005

arildno

I'll just post for a face change..

7. Feb 23, 2005

dextercioby

No face change needed...I can handle "winks"...

Daniel.