RE: Limit involving square root
- To: mathgroup at smc.vnet.net
- Subject: [mg30222] [mg30204] RE: [mg30167] Limit involving square root
- From: Bradley Stoll <BradleyS at Harker.org>
- Date: Fri, 3 Aug 2001 00:55:54 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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.
From: Hugh Goyder [mailto:goyder at rmcs.cranfield.ac.uk]
To: mathgroup at smc.vnet.net
Subject: [mg30222] [mg30204] [mg30167] Limit involving square root
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
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