Module 2
: Limits and Continuity of Functions
Lecture
5
:
Continuity
5.2 .5
Theorem:
Let
with
. For
, if
is continuous at
and
is continuous at
, then
is continuous at
.
Proof:
Let
.
Then, by the continuity of
.
Now, by the continuity of
.
Thus,
is continuous at
.
Back
1
2
3
4
5
6
7
8
9
10
11
12
with 
. For 
, if 
is continuous at 
and 
is continuous at
, then 
is continuous at 
. 
. 
. 
is continuous at 
. 
