Introduction to Limits

Formula for limits:

f(x) becomes closer to L as x moves towards a from the left or right.

The limit of f(x) as x approaches a is L.

Example:

 

As x approaches 2, f(x) is 1. The limit is 1.  

The limit does not exist when...

1. f(x) approaches a different number from the right side of c than from the left side of c.

     - You can see below that the limit does not exist at 0 because there is a jump in the graph.

2. When the graph tends to infinity.

    - As x aproaches 3 f(x) aproaches ∞, therefore the limit does not exist.

 

3. If f(x) oscillates between two values as x aproaches c.