On 9 Mai, 02:48, Ralf Bader <ba...@nefkom.net> wrote: > Virgil wrote: > > In article > > <1811b43c-f280-4075-86f4-efac30070...@y5g2000vbg.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > >> On 8 Mai, 21:56, Virgil <vir...@ligriv.com> wrote: > >> > In article > >> > <15ddac8c-14be-485b-bac7-213b078c1...@k8g2000vbz.googlegroups.com>, > > >> > 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.) > > What n? The natural numbers? What has the > behaviour of the function at infinity to do with calculating the derivative > at a finite point?
You seem to be surprised. It must be long time ago or never, that you learned calculus and the most trivial examples?
> >> 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. > > What does this have to do with the above? Did the n's mutate into x_n's or > what?
> > But that one sequence gives a limit does not guarantee that that > > sequence need give the same result as any other sequence.
Therfore I said "for every sequence (x_n) with limit x_0." > > Mückenheim will understand neither this nor that he need not teach you how > derivatives are defined (and even if, he could not, because he obviously > does not understand it himself)
Don't conclude from your state of understanding on that of authors of best selling text books. > > > 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. > > If Mückenheim's crap would be correct, then one could do with just one > sequence, appropriately chosen, in the definition of differentiability.
This proves your absolute ingnorance. Appropriately? What would that be in mathematics? The simplest counter-example is the function f(x) = |x| at x = 0. And there are other examples, for instance the function f(x) = 1 for x = 1/n, n in |N, and f(x) = 0 else.
We see: you do not even know the most simplest foundations of trivial mathematics, butyou try to understand advanced texts and to judge about uncomprehended mathematics. Ridiculous!