One-Sided Limit

Left Sided Limit or Left Hand Limit

Left Side Limit

Left Hand Limit

Right Sided Limit or Right Hand Limit

Right Side Limit

Right Hand Limit

The limit of a function at a point if it exists, is unique.

Function

Function

Left Hand Limit

Right Hand Limit

In this case, it can be seen that the limit from both the left and right sided as x tends to 2 is 4.

The limit of the function is 4 as x tends to 2 even though the function has no value at x = 2.

To calculate the limit of a function at a point, it is not of importance what happens at that particular point, but what happens around it.

Example

Given the function:

Function

Calculate Limit.

Left Hand Limit

Right Hand Limit

The function has no limit at x = 0.