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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: [mg62737] Re: [mg62717] How would you evaluate this limit in Mathmatica
  • From: Robert Knighten <Robert at Knighten.org>
  • Date: Sat, 3 Dec 2005 05:40:39 -0500 (EST)
  • References: <200512021053.FAA17727@smc.vnet.net> <8A8DC437-E3C1-40BC-8931-560CBE0420A3@mimuw.edu.pl> <17297.16618.553367.11758@zeus.knighten.org> <DA64C18C-208C-410D-911D-874408C23E91@mimuw.edu.pl>
  • Sender: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski writes:

 > I am afraid I have no good ideas for tackling this without using the  
 > Taylor series. However, in any case, I think to deal with this type  
 > of situation students need to understand not only the mathematics  
 > behind it but the limitations of computer software. I find that  
 > students are at the beginning quite surprised that such an advanced  
 > and expensive program as mathematica is can't deal with such problems  
 > by itself, but (if I have time for this sort of thing, which I  
 > usually do not) I try to make them think themselves of how to design  
 > a algorithm or a method that would deal with such problems without  
 > human intervention. I think this approach is very enlightening but it  
 > requires that the mathematics should already be well understood. It's  
 > because of problem like this that I do not think that CAS systems are  
 > suitable for developing understanding of mathematics. I think they  
 > are good for illustrating mathematical ideas, particularly by means  
 > of graphics, and for performing tedious computations and  
 > manipulations once one has a good understanding of the mathematical  
 > concepts involved. I would be very wary, however, about suggesting  
 > progrms like Matheamtica as a good means of undestanding limits,  
 > derivatives and integrals. A good text book is a far more reliable  
 > tool for this.

This discussion arose when the orignal poster offered this as an example of
how CAS can be tricky to use.  In particular he had collected examples of
problems that students had brought from other classes and tried to solve using
Mathematica.  He argued much as you do, and I was quite surprised that there
was some argument to the contrary.  That was what prompted me to post this to
the newsgroup.  So far I haven't seen any support for anything other than your
position.

Thank you again for your response.

-- Bob




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