2).
\The expression which is read as " The limit of
as
approaches
equals
"
In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behaviour of that function near a particular input.
\Informally, a function assigns an output to every input
.
The function has a limit at an input
if
is " close " to
whenever
is "close" to
.
In another words, become closer and closer to
as
move closer and closer to
.
More specifically, when is applied to each input sufficiently close to
, the result is an output value that is arbitrarily close to
.
If the inputs " close " to are taken to values that are very different, the limit is said to not exist.