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Error computing limits as x -> inf
10-09-2014, 03:52 PM
Post: #4
RE: Error computing limits as x -> inf
(10-09-2014 01:28 PM)Chris Pem10 Wrote:  I'd prefer that the calc not give me just enough rope to hang myself. If the HOME environment is not capable of performing limits at infinity, perhaps the calc should auto-magically substitute 1E50 for inf. And by substitution, I mean flash a warning that the substitution is happening and why.

Approximating infinity is a tricky business. 1E50 only works sometimes, for some problems. Some problems require a smaller value, because 1E50 would overflow. Other problems require a larger value, because 1E50 isn't big enough to converge on the desired result. And sometimes NO value suffices. Thinking and understanding are required on the part of the user. No machine can do that for you.

(10-09-2014 01:28 PM)Chris Pem10 Wrote:  It makes zero sense to have a working limit function in the CAS and a second version in HOME that fails.

I respectfully disagree. Expecting Home (which is a non-symbolic, floating-point approximation number cruncher only) to "understand" infinity (purely symbolic) reveals a misunderstanding of what Home is and how it works. Wanna crunch finite numbers in a 12-digit-approximation floating-point environment? Use Home. Wanna perform symbolic math on things like exact pi and infinity and undefined variables? Use CAS. They are different tools for different purposes.

(10-09-2014 01:28 PM)Chris Pem10 Wrote:  You cannot assume that the student will be smarter than the machine and capable of working around its quirks.

Assume? I assume nothing. I rather require ALL my students to be smarter than their calculators, and when they're not, I teach them well until they become smarter than their calculators. I fondly hope that the same expectation can be extended to the august membership of MoHPC.

Quirks? Behaviors which are unexpected due to misunderstanding of Prime are not quirks.

A general principle of tool usage is: If you don't understand a tool, it won't do what you want it to do. CAS and Home are two different tools, with different purposes, and with their own rules which must be understood to be used correctly. Home and CAS cannot be expected to be the same as each other; otherwise, why have both? The fact that Phillips screwdrivers strip flathead screws is not a bug in the design of Phillips screwdrivers, but rather reveals that the user does not understand the reason for the existence of both types of screws, and how and when to use their respective tools. Ok, that's a screwy analogy, but I hope you get my drift.

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RE: Error computing limits as x -> inf - Joe Horn - 10-09-2014 03:52 PM



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