Impressive(Original post by RoseGatz)
Got a question I'm a bit stuck on, care to help Zacken or anyone else for that matter? It's more pure stuff![]()
The functionis defined by
where
Show thatas
I've managed to show thatinstead of showing
, got no idea where the minus is coming from.
!
but in the negative sense, if you get me?
Look at the graph offor
to see why
diverges to
.
Although to be fair - if you have a limit that equals either plus or minus infinity, it's pretty much the same thing in that the limit does not exist.
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- 22-02-2016 19:31
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- 22-02-2016 19:43
(Original post by Zacken)
Impressive!
but in the negative sense, if you get me?
Look at the graph offor
to see why
diverges to
We went through this is class earlier today, we knew it was obviouslyconsidering the graph but is this just an assumption we make? Is there no way to explicitly get
or do we just go off assumption because of the graph?
(Original post by Zacken)
Although to be fair - if you have a limit that equals either plus or minus infinity, it's pretty much the same thing in that the limit does not exist. -
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- 22-02-2016 19:53
(Original post by RoseGatz)
Haha I know right! Took me a while to get the hang of it.
We went through this is class earlier today, we knew it was obviouslyconsidering the graph but is this just an assumption we make? Is there no way to explicitly get
or do we just go off assumption because of the graph?
is a shorthand way of saying that the limit doesn't exist, i.e: that it diverges. Having anything
nearly almost always never makes sense. So fussing about whether it's plus or minus infinity is something that we don't really tend to do because in either case - we're still just saying that the limit doesn't exist.
If you want some justification for why, you could try looking at
, might work - I haven't thought about it properly though, I'm rushing this out.
Most of the things you do with limits is based on epsilon-delta proofs, that is, the formal condition for limits and once you start working with infinity in there, that falls apart because you can't have something converge to infinity - so at this level, you're reduced to looking at graphs and making assumptions instead of working with things like you would in a real analysis course.
This: http://math.stackexchange.com/questi...nity-not-exist may shed some light on what I meant. -
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- 22-02-2016 20:00
Isn't the x^3 responsible for its divergence to -infinity, since as x approaches 0 ln(x) becomes large and negative therefore making the fraction small and negative?
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- 22-02-2016 20:04
(Original post by drandy76)
Isn't the x^3 responsible for its divergence to -infinity, since as x approaches 0 ln(x) becomes large and negative therefore making the fraction small and negative?is what causes the divergence to infinity.
is what causes the divergence to
. The user is enquiring as to the negative sign.
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- 22-02-2016 20:14
(Original post by Zacken)
is what causes the divergence to infinity.
is what causes the divergence to
. The user is enquiring as to the negative sign.
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