Limits Overview
Limit Notation (Left-Hand, Right-Hand, Overall)
Finding Limits Using a Graph
Finding a Limit Using Equations
Continuity

Example 1: Left Hand Limit

Determine lim x 2 f ( x ) =

Step 1: Draw a “wall” at the a value ( x value ) you are heading towards.

lim x 2 f ( x ) =

In this example we will draw the “wall” at x = 2 because that is the a value we are heading towards.

Step 2: Determine what type of limit you are being asked to evaluate. LHL ( ), RHL ( + ), or Overall .

In this example we have a negative sign ( ) in the exponent of our a value . So, we are being asked to find the Left-Hand Limit.

lim x 2 f ( x ) =

Step 3 ( LHL ): Begin drawing along your graph, f ( x ) , starting on the left side of the graph and moving to the right until you run into the “wall” you drew in Step 1 .

Notice that you do not care about any jumps in the graph as you do this. It is all one graph, f ( x ) . So, jump from one piece to the next and continue to follow the graph until you run into the “wall”.

The y value where you run into the wall is the answer to the question.

In this example we run into the “wall” at y = 1 .

So, the answer to our limit question is y = 1 .

Final Result:

lim x 2 f ( x ) = 1

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