Chapter 2

# Limits and Continuity

IN THIS CHAPTER

**Taking a look at limits**

**Evaluating functions with holes**

**Exploring continuity and discontinuity**

Limits are fundamental for both differential and integral calculus. The formal definition of a derivative involves a limit as does the definition of a definite integral.

## Taking It to the Limit

Let me say that another way. A function has a limit for a given *x*-value if the function zeroes in on some height as *x* gets closer and closer to the given value from the left and the right. It’s easier to understand limits through examples than through this sort of mumbo jumbo, so take a look at some.

### Three functions with one limit

Consider the function in Figure 2-1. When we say that the limit of as *x* approaches 2 is 5, written as , we mean that as *x* gets closer and closer to 2 from ...

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