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Re: Limit involving square root
*To*: mathgroup at smc.vnet.net
*Subject*: [mg30210] Re: Limit involving square root
*From*: "Carl K. Woll" <carlw at u.washington.edu>
*Date*: Thu, 2 Aug 2001 03:16:04 -0400 (EDT)
*Organization*: University of Washington
*References*: <9k880u$4vh$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi Hugh,
I don't know what's going wrong in your example, but there are two possible
remedies. First, there is a Calculus`Limit` package where Limit has been
enhanced. If you load this package and then try your limit, you will get the
correct result:
In[1]:=
<<Calculus`Limit`
In[2]:=
Limit[1+x-Sqrt[x^2-10x+9],x->Infinity]
Out[2]=
6
On the other hand, I prefer a different approach, using the Series command
as follows:
In[1]:=
Series[x-Sqrt[x^2-10x+9],{x,Infinity,3}]
Series[1+x-Sqrt[x^2-10x+9],{x,Infinity,3}]
Out[1]=
8 40 1 3
5 + - + -- + O[-]
x 2 x
x
Out[2]=
8 40 1 3
6 + - + -- + O[-]
x 2 x
x
As you can see (if you are using a fixed font), the Series command works
fine without introducing the Calculus`Limit` package.
Carl Woll
Physics Dept
U of Washington
"Hugh Goyder" <goyder at rmcs.cranfield.ac.uk> wrote in message
news:9k880u$4vh$1 at smc.vnet.net...
> Dear Mathgroup,
>
> Below I take the limit of a function and then the limit of 1 plus the same
> function. A plot of the function shows that the first result, (5), is
> correct but the second, (1), is wrong. (Should be 6.) What's happening?
>
> In[1]:=
> $Version
>
> Out[1]=
> 4.1 for Microsoft Windows (November 2, 2000)
>
> In[2]:=
> Limit[x - Sqrt[9 - 10 x + x^2],x -> Infinity]
>
> Out[2]=
> 5
>
> In[3]:=
> Limit[1 + x - Sqrt[9 - 10 x + x^2],x -> Infinity]
>
> Out[3]=
> 1
>
>
>
> I also note that using Series to expand about infinity does give the
> correct answers.
>
>
> Thanks
>
> Hugh Goyder
>
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