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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```

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