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MathGroup Archive 2007

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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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