Re: Series and Sqrt problem (a bug?)

• To: mathgroup at smc.vnet.net
• Subject: [mg86961] Re: Series and Sqrt problem (a bug?)
• From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
• Date: Thu, 27 Mar 2008 08:18:59 -0500 (EST)
• References: <fsd6o6\$9h0\$1@smc.vnet.net>

```GS <vokaputs at gmail.com> wrote:
> Numerically Mathematica defines square root of a positive number as a
> positive number:
> In[1]:= Sqrt[2.]
> Out[1]= 1.41421
>
> It is careful enough not to simplify a square root of a square:
> In[2]:= Sqrt[x^2]
> Out[2]= Sqrt[x^2]
> because x can be either positive or negative.
>
> However, when I specify that x approaches minus infinity, and use
> Series, it assumes that Sqrt[x^2] is equal to x:
> In[4]:= Series[Sqrt[x^2], {x, -Infinity, 1}] // Normal
> Out[4]= x
>
> It does the same thing when x approached plus infinity:
> In[5]:= Series[Sqrt[x^2], {x, Infinity, 1}] // Normal
> Out[5]= x
>
> This does not seem right to me, and caused grievances in my recent
> research problem.

In case it might help, note that

In[11]:= Assuming[a < 0,
Simplify[Normal[Series[Sqrt[x^2], {x, a, 1}]]]]

Out[11]= -x

David

```

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