FP3 Limits, Is My Answer Sufficient ?
Maths and statistics discussion, revision, exam and homework help.
-
- Reputation:
- Thread Starter
- Banned
- Posts: 891
FP3 Limits, Is My Answer Sufficient ?Q:
Show that
I go:
As
Hence as the denominator tends towards
then clearly 
Would that suffice as a valid answer ?
Secondly, and I would highly appreciate it if people could also answer this so that is completes my knowledge in the topic, if we have
then obviously that is undetermined, but if we have
then can it be said that as
?
Am I wright in thinking we can't write
because the limiting value must be finite and so we write
or
as
Thnx
Last edited by member910132; 09-05-2012 at 21:13. -
- Reputation:
- Exalted Member
- Posts: 304
Re: FP3 Limits, Is My Answer Sufficient ?Hi, firstly, it's fine to write that lim x ->0 1/x = infinity, or rather it would be if it were true (consider a limit approaching from the negative numbers (1/-1, 1/-0.1, 1/-0.01, ...)
You're saved in this limit because you're restricted to x>0 'cause of the lnx.
Edit: The edits are because I massively misread your post, sorry about that.Last edited by Jodin; 09-05-2012 at 20:13. -
- Reputation:
- Thread Starter
- Banned
- Posts: 891
Re: FP3 Limits, Is My Answer Sufficient ?Right, so is my answer to the first part of the question correct and sufficient ?(Original post by Jodin)
Hi, firstly, it's fine to write that lim x ->0 1/x = infinity, or rather it would be if it were true (consider a limit approaching from the negative numbers (1/-1, 1/-0.1, 1/-0.01, ...)
You're saved in this limit because you're restricted to x>0 'cause of the lnx.
Edit: The edits are because I massively misread your post, sorry about that. -
- Reputation:
- Peer Of The TSR Realm
- Location: Hungary
- Posts: 1,537
Re: FP3 Limits, Is My Answer Sufficient ?No.(Original post by member910132)
Q:
Show that
I go:
As
Hence as the denominator tends towards then clearly
Would that suffice as a valid answer ?
or 
are undefined.
Arranging F(x)
So if
the form of the limit will be
like
Use the L'Hospital rule.
..depending on the number set you are using.Secondly, and I would highly appreciate it if people could also answer this so that is completes my knowledge in the topic, if we have
then obviously that is undetermined,
For calculating limit we can use an extension of Reals including infinte ordinals
that is![\displaystyle \mathbb{R} \cup [-\infty, \infty]](http://www.thestudentroom.co.uk/latexrender/pictures/e3/e34da7a991e62d70875345b6ac55901f.png "\displaystyle \mathbb{R} \cup [-\infty, \infty]")
In this set
and
and f.e.
AS I noted above if we havebut if we have
then can it be said that as
?
and
through the positive reals or
through the negative reals
are two cases.
For the first
for the second
that is the
limit is not exists.
No. This limit is not exists in this form (in your Q x>0 because of lnx)Am I wright in thinking we can't write
because the limiting value must be finite and so we write
or
as
Thnx
Last edited by ztibor; 09-05-2012 at 21:00.
