A graphical illustration of the limit of a composite function

Abstract

In first‐year undergraduate calculus courses, students learn the concept of the limit of a function and the various limit laws for calculating the limits of functions. In this paper, we look at how a graphical method for composing functions can be used to give a geometric argument of the following theorem on limit of composite function: If f is continuous at b and limx→ag(x) = b, then limx→af(g(x)) = f (limx→ag(x)) = f (b).