Re: RE: Limit involving square root

*To*: mathgroup at smc.vnet.net*Subject*: [mg30246] Re: [mg30204] RE: [mg30167] Limit involving square root*From*: BobHanlon at aol.com*Date*: Fri, 3 Aug 2001 00:56:16 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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