 
Summary:
6.3.5
Study
Project:
Satisfying
requirements
on
limits
Barbara
A.
Shipman,
Active
Learning
Materials
for
a
First
Course
in
Real
Analysis
www.uta.edu/faculty/shipman/analysis.
Supported
in
part
by
NSF
grant
DUE0837810
Study
Project:
Satisfying
requirements
on
limits
In
this
study,
it
will
be
helpful
to
refer
to
the
definitions
of
limits
constructed
in
Discovery
Exercise:
Other
types
of
limits
of
functions.
1.
Functions
with
a
limit
on
only
one
side
a)
In
previous
work,
we
have
seen
that
a
function
that
is
not
defined
on
values
greater
than
p
cannot
have
a
righthand
limit
at
p.
Use
this
observation
to
construct
a
function
that
has
a
left
hand
limit
at
5
but
not
a
righthand
limit
at
5.
b)
Suppose
we
now
wish
to
consider
functions
defined
on
an
open
bounded
interval
around
5.
Find
an
unbounded
function
f : (0,10)
that
has
a
lefthand
limit
but
not
a
righthand
limit.
c)
If
possible,
find
a
bounded
function
g : (0,10)
that
has
a
lefthand
limit
but
not
a
right
