A. Limits (intuitive)

Intuitive Definition

The concept of the limit of a function is essential to the study of calculus. It is used in defining some of the most important concepts in calculus—continuity, the derivative of a function, and the definite integral of a function.

The limit of a function f( x) describes the behavior of the function close to a particular x value. It does not necessarily give the value of the function at x. You write lim f(x) = L
x - c

, which means that as x “approaches” c, the function f( x) “approaches” the real number L (see Figure 1).