# Push Your Limits

Evaluating Limits Using a Graph

In order for a limit to exist, the function much approach the same value from the left as it does from the right. For example, the limit as x approaches 2 does not exist in the example above. From the left the function value approaches 2, while from the right the function value approaches 3. However, the limit as x approaches 4 does exist. The function value approaches 2 from both the right and left, therefore the limit value is 2.

# Example 1

When we look at a limit at infinity, we are interested in the end behavior of the graph. To describe these limits we use the following notation: