Re: How would you evaluate this limit in Mathmatica
- To: mathgroup at smc.vnet.net
- Subject: [mg62727] Re: [mg62717] How would you evaluate this limit in Mathmatica
- From: Pratik Desai <pdesai1 at umbc.edu>
- Date: Sat, 3 Dec 2005 05:40:25 -0500 (EST)
- References: <200512021053.FAA17727@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Robert Knighten wrote: >There has recently been an off-topic discussion on the category theory mailing >list of the assertion that computer algebra systems are tricky to use >correctly. The starting point was the question of evaluating the (parametric) >limit: > >Lim ((1 + 4 x^2)^(1/4) - (1 + 5 x^2)^(1/5)) >x->0 --------------------------------------- > (a^(-x^2/2) - Cos[x]) > >So I am interested in getting comments about doing this in Mathematica. I'm >also interested in how one would teach solving limits using Mathematica. > > > How about something like this using Limit ? Looks like the parameter does not really play a big role in your limit evaluation?? Clear[x, a, denf, numf] numf[x_, a_] = ((1 + 4 x^2)^(1/4) - (1 + 5 x^2)^(1/5)); denf[x_, a_] = (a^(-x^2/2) - Cos[x]); Limit[numf[x, a]/denf[x, a], x -> 0, Direction -> 1] (*L'Hospital Rule*) Limit[D[numf[x, a], x]/D[denf[x, a], x], x -> 0, Direction -> -1] >>0 >>0 Regards, Pratik . -- Pratik Desai Graduate Student UMBC Department of Mechanical Engineering Phone: 410 455 8134
- References:
- How would you evaluate this limit in Mathmatica
- From: Robert Knighten <Robert@Knighten.org>
- How would you evaluate this limit in Mathmatica