Ministry of Higher Education
and Scientifics research
University of Babylon
College of Education for Pure Sciences
Physics Department
Three Stage
Complex Functions
2.3 Limits:Let
be defined and single-valued in a neighborhood of (It is
the set of all points
such that
where is positive real
number) with the possible exception of
it self. We say that the
number
is the limit of
as
approaches
and write
. "If for any positive number , we can find some
positive number
(depending on
)such that
whenever
".
In such case we also say that
approaches as approaches
and write
as
. We can represent the above definition
of limit by geometrical representation.
EX(1):- If
on
is defined
𝜔
prove that
ℓ
δ
by definition
Sol:- We see that 1 isn't belong to the
domain of
. Let
, then
where
1
ϵ
Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
College of Education for Pure Sciences
Physics Department
Three Stage
Thus
EX(2):- Prove that
Sol:-
Let
by def.
, then
EX(3):- If
 Limit of
Prove that
:- If we put the function 𝜔
new function
of function
. If
for all
, then
. That is when
when
? H.W
with
, we get a
to find the limit
suffice to the limit of function
.
EX:- Find
Sol:- Let
2