Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

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

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 258
Posted: May 8, 2013 4:43 PM

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.

The function f(x) = x has for every sequence x_n --> x_0 the sequence
of diference quotients
(x_n - x_0)/(x_n - x_0) = 1. The limit is 1 in all cases, and not 0.

Regards, WM