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limxx0

Limxx0 is an informal, wiki-style notation used in some educational and collaborative resources to denote the limit of a function as its argument approaches zero. It is not part of standard mathematical notation, but serves as a compact shorthand in contexts where the limiting process is clear from the discussion. When limxx0 f(x) appears, it is generally interpreted as the ordinary limit lim_{x→0} f(x).

Because limxx0 is informal, its precise meaning should be stated in each context. In many tutorials, limxx0

In multi-variable settings, limxx0 can be encountered to emphasize a limit as a single variable x tends

Reception and use: limxx0 is primarily a pedagogical device in community-driven resources and informal notes. It

is
used
to
illustrate
common
limits
without
repeating
the
full
lim
notation,
for
example
to
show
familiar
results
such
as
sin
x
/
x
approaching
1
or
(1+x)^{1/x}
approaching
e
as
x→0.
In
such
cases,
the
expression
is
understood
to
be
evaluated
by
the
standard
limit
process.
to
zero
while
other
variables
are
fixed
or
follow
a
specified
approach.
However,
this
usage
is
ambiguous
unless
the
limiting
path
or
conditions
are
specified.
Standard
notation
in
those
cases
would
be
lim_{x→0}
f(x,
y)
with
y
fixed,
or
lim_{(x,y)→(0,0)}
f(x,y)
if
both
variables
approach
zero.
can
aid
quick
demonstrations,
but
readers
should
verify
the
exact
definition
presented
in
any
given
text
to
avoid
misinterpretation.
See
also:
Limit
(mathematics);
One-sided
limit;
Multi-variable
limit.