Module 2
: Limits and Continuity of Functions
Lecture
4
:
Limit at a point
(ii)
Let
. We claim that
does not exist.
Suppose,
exists and the limit is
. Then, for
such that
.
In particular, for
,
.
That is,
for every
.
This is not possible, for example, we can choose positive integer
such that
, but
.
Hence,
does not exist.
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. We claim that 
does not exist. 
exists and the limit is 
. Then, for 
such that 
.
,
.
for every 
. 
such that
, but 
.
does not exist. 
