Hey guys not sure where to go with this, I am generally ok with delta epsilon questions but Im stuck here. I have a Summer test Thursday and supposedly something similar will come up.
Suppose that f(x) approaches L as x approaches a. Show that there corresponds to each positive number E (epsilson) a positive number d (delta) such that,
|f(x_{1})-f(x_{2})| < E
for every choice of x_{1}and x_{2 }in I( a, d ).
Sorry its on a pdf,
'We say that f has a limit L at a if, in the case of each positive number E, a positive number d can be found such that |f(x) - L| < E for every x element I'(a,d)
If f has a limit L at a we write
lim f(x) = L or f(x) approaches L as x approaches a
'
And thats it
I do not know how to use LaTex yet
'We say that f has a limit L at a if, in the case of each positive number E, a positive number d can be found such that |f(x) - L| < E for every x element I'(a,d)
If f has a limit L at a we write
lim f(x) = L or f(x) approaches L as x approaches a
If we drop the deleted neighborhood part then |f(x)-L| < E is always true, no restrictions?
So if it is true on the non-deleted neighborhood then for the same values it must be true on the deleted neighborhood. (this can be said for an infinite number of larger NDNs). And if true on the DN then |f(x1) - f(x2)| < E must be true?