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MathGroup Archive 2005

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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



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