Re: decoding inbuilt function

*To*: mathgroup at smc.vnet.net*Subject*: [mg121053] Re: decoding inbuilt function*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Thu, 25 Aug 2011 07:05:30 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201108221003.GAA22469@smc.vnet.net> <201108230948.FAA02694@smc.vnet.net> <CAO-JnY3cGaQi8qZ=8hb9sKkjb51HrbFPx+KjchnnWiQXj5iOfA@mail.gmail.com>*Reply-to*: murray at math.umass.edu

Nonsense! The student and I may both understand the definition of limit (which doesn't usually help to find the limit in the first place) and even know lots of theorems that do allow one to find a limit in various situations. But what a proprietary system does to implement finding limits is another matter entirely. For example, the algorithm used may be able to discern whether a function is a polynomial, or a composition of a list of basic built-in continuous functions, and then just use "direct substitution" -- that is, using that Limit[f[x],x->a] has value f[a]. You might wish to consult: http://reference.wolfram.com/mathematica/tutorial/TheAlgorithmsOfMathematica.html Taking derivatives is an entirely different matter! As every calculus instructor and every calculus student realizes, you don't have to know the definition of derivative as a limit of difference quotients in order to calculate derivatives. You just apply in some appropriate order a whole bunch of general rules -- addition formula, chain rule, etc. -- along with a known list of derivatives for basic elementary functions. Of course knowing which rules to apply and in which order is the trick. We humans have heuristics for doing that. But the way it's done by a "computer algebra system" may differ considerably from the way we do it with paper and pencil. Similarly, students learn how to do indefinite integration, with lots of heuristics involved as to what standard method to try. But a CAS may do things in a quite different way. In fact, I believe there's a considerable literature about that. Now if you're simply trying to rail against the very notion of a proprietary system, then I suggest you never use an operating system (other than Linux, etc.), never drive a modern automobile, never use a phone, .... On 8/23/11 8:43 PM, Ralph Dratman wrote: > If a student comes to your office saying she cannot seem to understand this > "limit" thingy, I wonder if you would wish to say, "Don't feel too bad, Ms > Liddell. No one in our department understands limits much better than you > do! Anyway, not enough to program a computer to do them. Only Wolfram has > the algorithm for that." > > This seems unconscionable to me. But then, I didn't realize taking limits > was so difficult. In order to differentiate something, obviously you have to > take a limit. Yet I never heard of anything one couldn't manage to > differentiate. And then having the derivative of a function would surely > help in taking other limits involving that function. What's the big > difficulty? > > Ralph > > > On Tuesday, August 23, 2011, Murray Eisenberg<murray at math.umass.edu> wrote: >> While you may get some hints about this, even from Wolfram Research >> employees, I suspect that there's proprietary information involved! >> >> On 8/22/11 6:03 AM, student wrote: >>> hi, >>> can any body please help me to decode the inbuilt function LIMIT in >>> mathematica or can any body please tell me how the inbuilt function >>> limit works and the logic behind it >>> please reply me soon as i really need that >>> >>> >>> >> >> -- >> Murray Eisenberg murray at math.umass.edu >> Mathematics& Statistics Dept. >> Lederle Graduate Research Tower phone 413 549-1020 (H) >> University of Massachusetts 413 545-2859 (W) >> 710 North Pleasant Street fax 413 545-1801 >> Amherst, MA 01003-9305 >> >> > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**decoding inbuilt function***From:*student <ragamadhuri.24@gmail.com>

**Re: decoding inbuilt function***From:*Murray Eisenberg <murray@math.umass.edu>

**Re: decoding inbuilt function**

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