Chapter 2

Limits and Continuity

IN THIS CHAPTER

Bullet Taking a look at limits

Bullet Evaluating functions with holes

Bullet 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

Math rules The limit of a function (if it exists) for some x-value, a, is the height the function gets closer and closer to as x gets closer and closer to a from the left and the right.

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 math 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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