MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: decoding inbuilt function

  • To: mathgroup at
  • Subject: [mg121053] Re: decoding inbuilt function
  • From: Murray Eisenberg <murray at>
  • Date: Thu, 25 Aug 2011 07:05:30 -0400 (EDT)
  • Delivered-to:
  • References: <> <> <>
  • Reply-to: murray at


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:

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>  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
>> 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
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

  • Prev by Date: Re: decoding inbuilt function
  • Next by Date: corner connected skeleton to face connected skeleton in 3d
  • Previous by thread: Re: decoding inbuilt function
  • Next by thread: Re: decoding inbuilt function