hi i was wondering if anyone could help me with this problem to do with limits. its a real anaylsis subject.
if g, defined on an interval [0,infinity), is decreasing function and is bounded below
then i want to show that lim x-> infinity g(x) exists.
can anyone help? thanks
hi i have another question, which i have attempted fully but i was wondering if someone could check it is right.
Suppose that lim x-> c f(x) = L where L >0, and that lim x-> c g(x) = infinity.
I want to show that lim x->c f(x)g(x) = infinity
Using properties of limits theorem
let f,g be real functions , lim x-> c f(x)g(x) = L x infinity
where L x infinity = infinity
hence lim x-> c f(x)g(x) = inifinity
can someone please check this thanks
so maybe my proof would go along these lines (i will not be formal):
we wish to find .
by theorem (so-and-so, whatever it is in your book),
.......i'm pretty sure there's a theorem for this last piece as well
(i would not write something like , that's just awkward)
Let be a sequence in converging to . Then we know that the sequence converges to and the sequence converges (abusing terminology) to . But this means because by the rule of sequence limits.