<s>
In	O
calculus	O
,	O
a	O
one-sided	B-Algorithm
limit	I-Algorithm
refers	O
to	O
either	O
one	O
of	O
the	O
two	O
limits	B-Algorithm
of	O
a	O
function	O
of	O
a	O
real	O
variable	O
as	O
approaches	O
a	O
specified	O
point	O
either	O
from	O
the	O
left	O
or	O
from	O
the	O
right	O
.	O
</s>
<s>
If	O
the	O
limit	O
of	O
as	O
approaches	O
exists	O
then	O
the	O
limits	B-Algorithm
from	O
the	O
left	O
and	O
from	O
the	O
right	O
both	O
exist	O
and	O
are	O
equal	O
.	O
</s>
<s>
does	O
not	O
exist	O
,	O
the	O
two	O
one-sided	B-Algorithm
limits	I-Algorithm
nonetheless	O
exist	O
.	O
</s>
<s>
It	O
is	O
possible	O
for	O
exactly	O
one	O
of	O
the	O
two	O
one-sided	B-Algorithm
limits	I-Algorithm
to	O
exist	O
(	O
while	O
the	O
other	O
does	O
not	O
exist	O
)	O
.	O
</s>
<s>
It	O
is	O
also	O
possible	O
for	O
neither	O
of	O
the	O
two	O
one-sided	B-Algorithm
limits	I-Algorithm
to	O
exist	O
.	O
</s>
<s>
If	O
represents	O
some	O
interval	O
that	O
is	O
contained	O
in	O
the	O
domain	B-Algorithm
of	O
and	O
if	O
is	O
point	O
in	O
then	O
the	O
right-sided	B-Algorithm
limit	I-Algorithm
as	O
approaches	O
can	O
be	O
rigorously	O
defined	O
as	O
the	O
value	O
that	O
satisfies	O
:	O
</s>
<s>
and	O
the	O
left-sided	B-Algorithm
limit	I-Algorithm
as	O
approaches	O
can	O
be	O
rigorously	O
defined	O
as	O
the	O
value	O
that	O
satisfies	O
:	O
</s>
<s>
In	O
comparison	O
to	O
the	O
formal	O
definition	O
for	O
the	O
limit	B-Algorithm
of	I-Algorithm
a	I-Algorithm
function	I-Algorithm
at	O
a	O
point	O
,	O
the	O
one-sided	B-Algorithm
limit	I-Algorithm
(	O
as	O
the	O
name	O
would	O
suggest	O
)	O
only	O
deals	O
with	O
input	O
values	O
to	O
one	O
side	O
of	O
the	O
approached	O
input	O
value	O
.	O
</s>
<s>
For	O
reference	O
,	O
the	O
formal	O
definition	O
for	O
the	O
limit	B-Algorithm
of	I-Algorithm
a	I-Algorithm
function	I-Algorithm
at	O
a	O
point	O
is	O
as	O
follows	O
:	O
</s>
<s>
To	O
define	O
a	O
one-sided	B-Algorithm
limit	I-Algorithm
,	O
we	O
must	O
modify	O
this	O
inequality	O
.	O
</s>
<s>
For	O
the	O
limit	B-Algorithm
from	I-Algorithm
the	I-Algorithm
right	I-Algorithm
,	O
we	O
want	O
to	O
be	O
to	O
the	O
right	O
of	O
,	O
which	O
means	O
that	O
,	O
so	O
is	O
positive	O
.	O
</s>
<s>
Similarly	O
,	O
for	O
the	O
limit	B-Algorithm
from	I-Algorithm
the	I-Algorithm
left	I-Algorithm
,	O
we	O
want	O
to	O
be	O
to	O
the	O
left	O
of	O
,	O
which	O
means	O
that	O
.	O
</s>
<s>
One	O
example	O
of	O
a	O
function	O
with	O
different	O
one-sided	B-Algorithm
limits	I-Algorithm
is	O
(	O
cf	O
.	O
</s>
<s>
The	O
one-sided	B-Algorithm
limit	I-Algorithm
to	O
a	O
point	O
corresponds	O
to	O
the	O
general	O
definition	O
of	O
limit	O
,	O
with	O
the	O
domain	B-Algorithm
of	O
the	O
function	O
restricted	O
to	O
one	O
side	O
,	O
by	O
either	O
allowing	O
that	O
the	O
function	B-Algorithm
domain	I-Algorithm
is	O
a	O
subset	O
of	O
the	O
topological	O
space	O
,	O
or	O
by	O
considering	O
a	O
one-sided	O
subspace	O
,	O
including	O
Alternatively	O
,	O
one	O
may	O
consider	O
the	O
domain	B-Algorithm
with	O
a	O
half-open	O
interval	O
topology	O
.	O
</s>
<s>
A	O
noteworthy	O
theorem	O
treating	O
one-sided	B-Algorithm
limits	I-Algorithm
of	O
certain	O
power	O
series	O
at	O
the	O
boundaries	O
of	O
their	O
intervals	O
of	O
convergence	O
is	O
Abel	O
's	O
theorem	O
.	O
</s>
