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MathGroup Archive 2001

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RE: Limit involving square root

  • To: mathgroup at
  • Subject: [mg30222] [mg30204] RE: [mg30167] Limit involving square root
  • From: Bradley Stoll <BradleyS at>
  • Date: Fri, 3 Aug 2001 00:55:54 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

Your eyes (and domain) are deceiving you.  At first glance, I thought the
result to the first function should've been zero.  Then after evaluating, at
what I thought were very large numbers, I thought I was mistaken and indeed
the answer was 5.  But further investigations reveal that the first limit is
in fact 0.  Try this to see something interesting.  Evaluate at 10^15, 10^16
and 10^17.  I think you will be surprised.  Also, I tried using Mathematica
4.1 to evaluate the first limit directly and it just gave me back my input.

Bradley Stoll

-----Original Message-----
From: Hugh Goyder [mailto:goyder at]
To: mathgroup at
Subject: [mg30222] [mg30204] [mg30167] Limit involving square root

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?


4.1 for Microsoft Windows (November 2, 2000)

Limit[x - Sqrt[9 - 10 x + x^2],x -> Infinity]


Limit[1 + x - Sqrt[9 - 10 x + x^2],x -> Infinity]


I also note that using Series to expand about infinity does give the
correct answers.


Hugh Goyder

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