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Limit involving square root

• To: mathgroup at smc.vnet.net
• Subject: [mg30167] Limit involving square root
• From: Hugh Goyder <goyder at rmcs.cranfield.ac.uk>
• Date: Wed, 1 Aug 2001 02:19:22 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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