For example, f(x) has a unilateral limit at x=x0. When finding the left limit or right limit of f(x) at x=x0, generally, x=x0 is directly substituted into f(x) to get f(x0), and then simplified. Note that no matter whether the domain is open or closed, there is only a unilateral limit at the end of the interval.

Extended data:

Left limit and right limit:

1, definition

Suppose it is a function defined on an interval, if the following criteria hold:

Given arbitrarily, you can find everything that satisfies the inequality. It is said that it converges to the limit when it tends from the left. Remember as.

The numerical value is the distance between and, and we can think of it as an approximate representation of the error. Therefore, this definition is equivalent to assertion, and the error caused by approximate representation can be as small as we arbitrarily specify, as long as it is close enough to the coordinates.

2. Unilateral limits and limits

The left and right limits are collectively referred to as unilateral limits. When the function exists, the limit exists, and if and only if the function exists, both the left limit and the right limit exist and are equal. Expressed by mathematical expressions: existence and both existence and sum.