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limit of a function

In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input. Formal definitions, first devised in the early 19th century, are given below. Informally, a function $f$ assigns an output $f (x)$ to every input $x$ . We say that the function has a limit $L$ at an input $p$ , if $f (x)$ gets closer and closer to $L$ as $x$ moves closer and closer to $p$ . More specifically, when $f$ is applied to any input sufficiently close to $p$ , the output value is forced arbitrarily close to $L$ . On the other hand, if some inputs very close to $p$ are taken to outputs that stay a fixed distance apart, then we say the limit does not exist.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Limit_of_a_function)

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