When we define the limit of a function, do we first require the function to be defined in the centripetal domain of x0, and the root sign is not negative, so we require the definition domain of x≥0, so why use ? x-x0 ?≤ x0 to ensure it? First of all, we don't know what x0 is. I can say that you can think it is a big positive number or a small positive number. Maybe you think too much. If you expand the absolute value, you will have the question of why X is limited to 2x0 at the same time. First, when we define the limit, we only need to define it in the core field of x0, and I don't care about other definitions. The so-called coring field is a small and pitiful interval, which can be defined by X less than 2x0. Secondly, when we define the eccentric field, we use the definition of absolute value, and the geometric meaning of absolute value represents distance.

So we can make the following summary: When proving the limit of a function, if X approaches x0 and x0 is arbitrary, we should consider the domain of the function, and the method of defining the domain of the function is limited by the distance represented by the absolute value.