1.2 Defining Limits and Using Limit Notation

🎥Watch: AP Calculus AB/BC - Graphical Limits

A limit is the y value a function approaches as it approaches a certain x value. You will usually see limits in this notation: 📈

This means that as x approaches a, on the graph of f(x), the value on the y-axis that the function approaches is L.

To understand limits better, let’s look at the function f(x) = x + 1. 🖋

The limit of f(x) as x approaches 4 is the value f(x) approaches as we get closer and closer to x = 4. If we were to graph f(x), this is the y-value we approach when we look at the graph of f(x) and get closer and closer to the point on the graph where x = 4.

For example, if we start at the point (1, 2) and move on the graph until we get really close to x = 4, then our y-value gets really close to 5. Similarly, if we start at (6, 7) and move closer to x = 4, the y-value gets closer and closer to 5. Thus, the limit of f(x) as x approaches x = 4 is 5.