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Re: RE: Limit involving square root


In a message dated 2001/8/2 5:14:39 AM, BradleyS at Harker.org writes:

>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.
>

The limit is 5.  You are getting numerical errors due to machine precision.  
Use extended precision.

N[(x - Sqrt[9 - 10 x + x^2]) /. { {x -> 1*^15}, {x -> 1*^16}, {x -> 
          1*^17}, {x -> 1*^18}}, 50]

The limit is easier to understand if you write the expression as

x-Sqrt[(x-5)^2-16]


Bob Hanlon
Chantilly, VA  USA


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