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Re: Re: Re: More about l`Hopital`s rule
*To*: mathgroup at smc.vnet.net
*Subject*: [mg24720] Re: [mg24683] Re: [mg24623] Re: More about l`Hopital`s rule
*From*: Rob Pratt <rpratt at email.unc.edu>
*Date*: Wed, 9 Aug 2000 02:31:18 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
John,
I see now that when you said "limit in the book which doesn't approach a
number, ..." you were referring to 'a' in Limit[f[x], x -> a] = L, and I
had thought you were talking about L.
Sorry for the confusion.
Rob Pratt
Department of Operations Research
The University of North Carolina at Chapel Hill
rpratt at email.unc.edu
http://www.unc.edu/~rpratt/
On Fri, 4 Aug 2000, John D. Hendrickson wrote:
> I explored the problem as I did to make it clear to the "newbie" that his
> "simple limit" was not simple because it asked Mathematica not to solve a
> regular limit but to solve "A FAMILY OF LIMITS".
>
> First off, I did not say that the results of limits were never functions in
> the book. Read what you pasted again.
>
> With respect to "the mention of the definition of derivitives" I am still
> justified in what I said.
>
> Definition (3.1) contained:
> "the slope of the tangent line of a function 'f' at P(a,f(a)) is
> Limit[ f(a+h)-f(a), h->0] provided the limit exists"
> and is repeated numberous times in different ways.
>
> The "alternate" definition (3.6):
> Limit[ f[x] - f[a] / (x-a), x->a ]
> followed from a discussion of a ""the slope of the line pq" on a graph, in
> which x==(a+h) is then substituted and used as the formal definition (3.1),
> where 'h' approaches the number 0.
>
> The "alternate definition" is not used in either the example problems or
> homework problems for those sections. So, as I suggested, such a thing was
> not presented as a topic of use for limiting taking purposes in the book, so
> far as I can see, yet.
>
> I've delete quite a bit of my response because it was lengthy for purpose.
> I'll just say that those sections are characterised by a kind of limit that
> pproaches 0 through 'h'.
>
> I do not wonder that by brushing through the whole book I might have missed
> a few good examples (which I have not yet seen). I did say "as far as I can
> see".
>
>
> Rob Pratt wrote in message <8m3vgo$dju at smc.vnet.net>...
> >> I Took my four Calculus courses out of Swokowski's Calculus book (the
> whole
> >> book). And looking back - I don't see a single limit in the book which
> >> doesn't approach a number, constant of a definite integration, or
> infinity.
> >
> >Think you better take a closer look, John. I don't have my copy of
> >Swokowski in front of me, but I can say with confidence that it contains
> >numerous limits whose results are functions. In particular, this happens
> >any time the definition of a derivative is mentioned.
> >
> >Rob Pratt
> >Department of Operations Research
> >The University of North Carolina at Chapel Hill
> >
> >rpratt at email.unc.edu
> >
> >http://www.unc.edu/~rpratt/
> >
> >
>
>
>
>
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