Chapter 12.1: Introduction to Limits

This next chapter is all about limits. So the first question was, what is a limit?
The book defines a limit as:

If f(x) becomes arbitrarily close to a unique number L, as x approaches c from either side, the limit of f(x) as x approaches c is L.

More simply, a limit is the value y approaches as x approaches a specified value.

 

 

Today we learned two different ways of finding the limit:

1. Tables

2. Graphs



 

First, insert the equation into your calculator.

Then insert values into the table that are close to 2.

From this table, you can tell that as x approaches 2, y approaches 5. So the limit is 5.

From the graph, we can see that as x approaches 0, y approaches 1. All these types of problems are solved by just looking at the graph.

Limits That Do Not Exist:
There are also limits that don't exist. There are 3 scenarios where this happens.

1. When y approaches two different numbers
-In the example above, if you try to solve for the limit when x approaches 1, you get two values that y approaches. Therefore, there is not a limit at all.

2. When y approaches infinity or negative infinity
-In the graph below, as x approaches 1, y approaches both infinity and negative infinity. In this example, the limit DNE.
 

 3. In oscillating graphs
-In the graph of sin(1/x), the wave only goes between 1 and -1 so there is no limit.

That's mostly everything we learned today. Hope it helped!
-Natalie