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Topic: Matheology � 258
Replies: 53   Last Post: May 11, 2013 10:07 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 258
Posted: May 8, 2013 5:21 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 8 Mai, 21:56, Virgil <vir...@ligriv.com> wrote:
> > In article
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > For all n: f(n) = 1 , lim_n-->oo f(n) = 1
> > > This is required for correctly calculating differential quotients in
> > > analysis. (Just this morning I explained that in class.)

> >
> > My sympathy for your poor students to be subjected to such incompetence.
> >
> > Curious that that particular limit appears so rarely in calculating
> > differential quotients or in calculus texts.
> >
> > One does not find it referred to at all in such calculus texts as
> > Apostol.
> > --

>
> If for every sequence (x_n) with limit x_0 the limit of the sequence
> of difference quotients
> (f(x_n) - f(x_0))/(x_n - x_0) exists and is the same in all cases,
> then df/dx is defined at x_0.

But that one sequence gives a limit does not guarantee that that
sequence need give the same result as any other sequence.

So unless one has some other guarantee of differentiability at the point
in question, finding a supposed derivative or slope by a sequence is not
guaranteed to work right.
--