A limit from just one side of a point is used when the limit does not exist. This happens when the function approaches a value from one side but not from the other.

Right Sided Limit

The right sided limit of a function is the limit of the function as approaches from the right side and is denoted as .

Example

The right sided limit as approaches is shown as the red dot. In a formula this would be denoted as .

Left Sided Limit

The left sided limit of a function is the limit of the function as approaches from the left side and is denoted as .

Example

The left sided limit as approaches is shown as the red dot. In a formula this would be denoted as .