On 8 Mai, 23:21, Virgil <vir...@ligriv.com> wrote: > In article
> > 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.
That's why I said "for every" sequence.
You seem nearly as uninformed and unskilled as Bader.