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MathGroup Archive 1996

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Strange Behaviour of Limits[...]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5165] Strange Behaviour of Limits[...]
  • From: jeyadev at wrc.xerox.com
  • Date: Wed, 6 Nov 1996 01:34:25 -0500
  • Organization: Deja News Usenet Posting Service
  • Sender: owner-wri-mathgroup at wolfram.com

I wrote to this newsgroup sometime ago about this, but there was no
response. Hope someone bites this time! I would prefer to, at the least,
receive a copy of any response by email as the news feed may miss
the posted response.

As a new user of Mathematica, I am having some difficulty is getting the
correct limit (and hence, the correct Taylor series expansion of a
very simple function. I have done this kind of thing in Macsyma without
any difficulty, but am unable to find what I am doing wrong. What I need
is the following limit:

                lim      Sqrt[a^2 + x^2] - a
                        ---------------------
               x -> 0    Sqrt[b^2 + x^2] - b


It does not take much to work out the answer: it is   b/a.

Using Mathematica's Limit[..., x ->0] I get


                      a - Sqrt[a^2]
                      -------------
                      b - Sqrt[b^2]

Greatly disappointed with this, I next tried to Taylor expand the 
expression as a function of x around x = 0. Needless to say, the
same sort of terms as above occurred as coefficients in the expansion
coefficients contained indeterminate fractions as the one given above.

In the first case, is appears the Mathematica is doing a simple x = 0
substitution. I have used Macysma rather extensively to do Taylor
expansions of complicated functions, and it has never done anything
like this. So, is there some "switch" I have to turn on? Or ...


thanks
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