Module 2
: Limits and Continuity of Functions
Lecture
4
:
Limit at a point
5.
Let
be such that for some
. Does this imply that
exists? Analyze the converse.
6.
Let
where
are real numbers with
. Show that
and that
if
and
while
if
and
.
7.
Let
for all
, where
. If
, show that
.
8.
Let
and
. Prove that if
, then there is some
such that
for all
.
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be such that for some 
. Does this imply that 
exists? Analyze the converse. 
are real numbers with 
. Show that 
if 
and 
while 
if 
and 
. 
for all 
, where 
. If 
, show that 
. 
and 
. Prove that if 
, then there is some 
such that 
for all 
. 
