<s>
In	O
mathematics	O
,	O
the	O
approximate	B-Algorithm
limit	I-Algorithm
is	O
a	O
generalization	O
of	O
the	O
ordinary	O
limit	B-Algorithm
for	O
real-valued	O
functions	O
of	O
several	O
real	O
variables	O
.	O
</s>
<s>
A	O
function	O
f	O
on	O
has	O
an	O
approximate	B-Algorithm
limit	I-Algorithm
y	O
at	O
a	O
point	O
x	O
if	O
there	O
exists	O
a	O
set	O
F	O
that	O
has	O
density	O
1	O
at	O
the	O
point	O
such	O
that	O
if	O
xn	O
is	O
a	O
sequence	O
in	O
F	O
that	O
converges	B-Algorithm
towards	O
x	O
then	O
f(xn )	O
converges	B-Algorithm
towards	O
y	O
.	O
</s>
<s>
The	O
approximate	B-Algorithm
limit	I-Algorithm
of	O
a	O
function	O
,	O
if	O
it	O
exists	O
,	O
is	O
unique	O
.	O
</s>
<s>
If	O
f	O
has	O
an	O
ordinary	O
limit	B-Algorithm
at	O
x	O
then	O
it	O
also	O
has	O
an	O
approximate	B-Algorithm
limit	I-Algorithm
with	O
the	O
same	O
value	O
.	O
</s>
<s>
Many	O
of	O
the	O
properties	O
of	O
the	O
ordinary	O
limit	B-Algorithm
are	O
also	O
true	O
for	O
the	O
approximate	B-Algorithm
limit	I-Algorithm
.	O
</s>
<s>
In	O
particular	O
,	O
if	O
a	O
is	O
a	O
scalar	O
and	O
f	O
and	O
g	O
are	O
functions	O
,	O
the	O
following	O
equations	O
are	O
true	O
if	O
values	O
on	O
the	O
right-hand	O
side	O
are	O
well-defined	O
(	O
that	O
is	O
the	O
approximate	B-Algorithm
limits	I-Algorithm
exist	O
and	O
in	O
the	O
last	O
equation	O
the	O
approximate	B-Algorithm
limit	I-Algorithm
of	O
g	O
is	O
non-zero	O
.	O
)	O
</s>
<s>
has	O
an	O
approximate	B-Algorithm
limit	I-Algorithm
as	O
h	O
approaches	O
zero	O
we	O
say	O
that	O
f	O
has	O
an	O
approximate	O
derivative	O
at	O
x0	O
.	O
</s>
