- #1
allergic
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Since the function f(x)=xsin[(pi)x] oscillates, shouldn't the limit as x -> infinity not exist? i was told that it is positive infinity.
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Homework Help Overview
The discussion revolves around finding the limit of the function f(x) = xsin(πx) as x approaches infinity. Participants are exploring the behavior of this oscillating function and its implications for the existence of the limit.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Some participants question whether the limit exists due to the oscillatory nature of the function. Others suggest that the role of π in the function's argument may not be significant. There is also a consideration of whether x is treated as an integer, which could affect the limit's existence.
Discussion Status
The discussion is active, with participants offering different perspectives on the limit's existence. There is no explicit consensus, but several interpretations are being explored regarding the nature of the variable x and its implications for the limit.
Contextual Notes
Participants are discussing the function's behavior under different assumptions about the variable x, including whether it is treated as an integer or a real number. The implications of these assumptions on the limit are being examined.
- #2
arildno
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If your function really is [tex]f(x)=x\sin(\pi{x})[/tex] , then you're right.
(That is, a limit doesn't exist)
(That is, a limit doesn't exist)
Last edited:
- #3
dextercioby
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Note,that "pi" in the argument is totally unimportant.A certain rescaling would eliminate it...
Daniel.
Daniel.
- #4
arildno
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Unless, of course, x is supposed to be an integer variable; in which case a limit does exist..
- #5
dextercioby
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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.
Daniel.
- #6
arildno
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I'll just post for a face change..
- #7
dextercioby
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No face change needed...I can handle "winks"...
Daniel.
Daniel.