4.1 Introduction

When we hear the word “limit,” we think of the maximum ability or capacity of something. In mathematics, a limit is the value that a function approaches as the independent variable or the input variable approaches a certain value. The limits help us understand the behaviors of functions at a particular point. Limits are also important in calculus and mathematical analysis. We use limits in calculus to define derivatives (discussed in the next chapter), integrals, and continuity.

In this chapter, we are going to introduce the definition of limits and explain how we can use the limits to understand the behavior of a function.