1.3 Estimating Limit Values from Graphs

🎥Watch: AP Calculus AB/BC - Graphical Limits

This topic centers around the difference between the value a function is approaching (limits) and the value of the function itself. Graphs are a great way to help visualize the difference between these two concepts.

In the graph above, we can show the difference between the value a function is approaching and the actual value of the function. Starting on the left side of the function and moving toward x = 4, we can see that the y value gets closer to y = 5. Starting on the right side and moving backward to x = 4, we also get closer to y = 5. However, if we try to evaluate the function AT x = 4 we get y = 4. This is the key difference between the value a function is approaching and the value of the function itself. In this example, the limit is 5 but the value of f(4) is 4. 🤓

The big takeaway from this example is that the value of a function at a particular value does not (✖) mean that the limit value is the same.

As you saw in the example above, we estimate a limit value in a graph by approaching the x value from both sides. Here are the steps needed to estimate the limit value: 

If you’re still confused, take a look at the pictures below. 📷