> 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? > > Consult an introductory text on analysis, for instance my book > http://www.amazon.de/Mathematik-Physik-10-2012-ersten-Semester/dp/348670821X/ref=sr_1_4?s=books&ie=UTF8&qid=1368086437&sr=1-4&keywords=M%C3%BCckenheim > >> > 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! > > Regards, WM
Blablablabla. Your idiotic crap
|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.)
remains idiotic crap even if you again prove your competence (the only one to be seen in your 28thousandandsomething postings) in idiotic libels.