Module 2
: Limits and Continuity of Functions
Lecture
4
:
Limit at a point
4.1 .3
Theorem (Algebra of limits):
Suppose
and
exist. Then the following hold:
(i)
.
(ii)
.
(iii) For any real number
.
(iv) If
Proof:
Follows from the Limit Theorems for sequences. We leave the details as an exercise.
Back
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and 
exist. Then the following hold: 
. 
. 
. 
