Normal for Limit : Example
- To: mathgroup at smc.vnet.net
- Subject: [mg74344] Normal for Limit : Example
- From: Mr Ajit Sen <senra99 at yahoo.co.uk>
- Date: Mon, 19 Mar 2007 02:04:49 -0500 (EST)
Dear Sebastian,
Here is an example to illustrate what I meant:
f=(2x-5)/ (x-2)
Limit[f,x -> 3] ---> 1
Both agree here.
Normal[f+O[x,3]] ---> 1
However, at the point of discontinuity x = 2 (which
I
referred to loosely as a "pole" : I find the whole
thing redolent of Laurent Series),
Limit[f,x -> 2] ---> - Infinity [Correct]
Normal[f+ O[x,2]] ---> 2 - 1/(-2+x) [ = f ]
Now, I've always been using Normal to get rid of the
O[ ] terms in Series, and I found Andrzej's
alternative use of Normal rather neat, although I
have no idea how it works. Trace doesn't help me
much
here. So, the question is whether Normal can be
used
at a point of discontinuity.
BTW, my query was prompted by Eric Smith's posts on
Limit.
Best Regards.
Ajit Sen.
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