Chapter 7
Limits and Continuity
In This Chapter
Taking a look at limits
Evaluating functions with holes — break out the mothballs
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. (If you’re a real go-getter and can’t wait to read the actual definitions, check out Chapters 9 and 13.) Now, it turns out that after you learn the shortcuts for calculating derivatives and integrals, you won’t need to use the longer limit methods anymore. But understanding the mathematics of limits is nonetheless important because it forms the foundation upon which the vast architecture of calculus is built (Okay, so I got a bit carried away). In this chapter, I lay the groundwork for differentiation and integration by exploring limits and the closely related topic, continuity.
Take It to the Limit — NOT
Limits can be tricky. Don’t worry if you don’t grasp the concept right away.
Informal definition of limit (the formal definition is in a few pages): ...
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