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Re: How would you evaluate this limit in Mathmatica
*To*: mathgroup at smc.vnet.net
*Subject*: [mg62770] Re: How would you evaluate this limit in Mathmatica
*From*: p.ramsden at imperial.ac.uk
*Date*: Mon, 5 Dec 2005 03:37:10 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Yeah, I actually think this is a lovely example of how "teaching using a CAS" can potentially work really *well*. If the CAS is used as a supposedly infallible, oracular source of correct answers, than obviously there's a problem. So let's not use Mathematica like that! We shouldn't be using it like that anyway. That's what the back of textbooks is for.
Instead, how about a sequence of activities that, for example, asks students to use Mathematica to evaluate the generic limit and then the exceptional case, and then invites them to comment on any discrepancy, investigate and try to work out what's going on, using whatever techniques and resources they like (graph plotting, series expansion, L'Hopital's Rule, etc). That's potentially a really nice open-ended problem that could even form the basis of a mini-project. And if one of the things that comes out of it is that software isn't infallible, so much the better.
Indeed, the question why this is a hard problem to solve using generic algorithms is itself quite rich and interesting, don't you feel?
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