Re: Strange Behaviour of Limits[...]

• To: mathgroup at smc.vnet.net
• Subject: [mg5283] Re: [mg5165] Strange Behaviour of Limits[...]
• From: leejunho <leejunho at soback.kornet.nm.kr>
• Date: Mon, 18 Nov 1996 02:30:38 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```jeyadev at wrc.xerox.com wrote:
>
> 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.  Is there some "switch" I have to turn on? Or ...
>
> thanks
> -----------------------------------------------------------------------
> This article was posted to Usenet via the Posting Service at Deja News:
> http://www.dejanews.com/          [Search, Post, and Read Usenet News!]

In the equation you have tried, not only "x" but alse "a"and"b"
are variable in Mathematica. so then "a"and"b" is reft in variable.

If "a" and "b" are changed by numbers, the result of the calculation
will be right.

[[A example]]

In[3]:=
Limit[ (Sqrt[a^2 + x^2] - a)/(Sqrt[b^2 + x^2] - b),x->0]
Out[3]=
2
a - Sqrt[a ]
------------
2
b - Sqrt[b ]

In[4]:=
a=2;b=3;

In[6]:=
Limit[ (Sqrt[a^2 + x^2] - a)/(Sqrt[b^2 + x^2] - b),x->0]
Out[6]=
3
-
2

In[7]:=
a=1+3I;b=1+2I;

In[8]:=
Limit[ (Sqrt[a^2 + x^2] - a)/(Sqrt[b^2 + x^2] - b),x->0]
Out[8]=
7    I
-- - --
10   10

In[9]:=
b/a
Out[9]=
7    I
-- - --
10   10

=============================
Lee Junho
leejunho at soback.kornet.nm.kr
Pusan.Korea
=============================

```

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