Introducing the concept of a Limit. Definition: The Limit of a function (f(x)) as (x) approaches a value (a) is the value that (f(x)) gets closer to as (x) gets closer to (a).Calculus requires an understanding of limits since it is the foundation for the concepts of continuity, derivatives, and integrals. A function's behavior as its input (or argument) gets closer to a given value is described by a limit. Example:Let's begin to formulate an intuitive concept of the limit based on this very brief informal examination of one limit. If there is a real number L that the functional values approach as the x-values approach a, we can think of the limit of a function at a number an as being that one real number.Understanding how Limits work 1. Approaching a Point: Consider (x) getting closer to a point (a) from both sides (left and right). 2. Observing the Function's Output: As (x) gets closer to (a), what value does (f(x)) approach?Example of Limits of Function.