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Re: Series and Sqrt problem (a bug?)


Hi,

using Abs[x] instead of Sqrt[x^2]
may help.

Regards
   Jens

GS 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.
> GS
> 


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