The limit of a function at a point aa in its domain (if it exists) is the value that the function approaches as its argument approaches a. The concept of a limit is the fundamental concept of calculus and analysis. It is used to define the derivative and the definite integral, and it can also be used to analyze the local behaviour of functions near points of interest. Limit, mathematical concept based on the idea of closeness, used primarily to assign values to certain functions at points where no values are defined, in such a way as to be consistent with nearby values.