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:

Example 2

Example 3

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