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/ > > > > > > > >