Chapter 15

Scouting the Road Ahead to Calculus

In This Chapter

arrow Determining limits graphically, analytically, and algebraically

arrow Pairing limits and operations

arrow Identifying continuity and discontinuity in a function

Every good thing must come to an end, and for pre-calculus, the end is actually the beginning — the beginning of calculus. Calculus is the study of change and rates of change (not to mention a big change for you!). Before calculus, everything had to be static (stationary or motionless), but calculus shows you that things can be different over time. This branch of mathematics enables you to study how things move, grow, travel, expand, and shrink and helps you do so much more than any other math subject before.

This chapter helps prepare you for calculus by introducing you to the very first bits of the subject. First, we run through the difference between pre-­calculus and calculus. Then we look at limits, which dictate that a graph can get really close to values without ever actually reaching them. Before you get to calculus, math problems always give you a function f(x) and ask you to find the y value at one specific x in the domain (see Chapter 3). But when you get to calc, ...

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