Limit of a function

From Mathematics

The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of the function near a particular value of its independent variable.

The limit of a function at is if for every , there exists a such that implies .

That is, if is within any arbitrary distance of whenever is sufficiently close, but not necessarily equal to, .

Note that represents the greatest distance between the values of the function and its limit, while represents the distance from the values of the function's inputs to .

The idea that the condition is not required allows for the possibility that the values of function approaches , but the actual value of need not be , or even defined.

If, by chance, we have , then we also say that is continuous at .