Limit is an important concept in mathematics, which is used to describe the trend of a function or sequence at a certain point or at infinity. You can first understand the definition of the following restrictions:

1. Definition of function limit:

Let the function f(x) be defined in a neighborhood of x = A. If there is a positive number δ for any given positive number ε, then when 0

lim┬(xa)？ 「f(x) = L」

Where l is a constant.

This definition shows that when the independent variable of X is close to A, the value of function f(x) will be infinitely close to L. It can be understood that no matter how close to A, as long as it is close enough to A, the difference between function value and L can be controlled within ε.

2. The definition of sequence limit:

Let the elements in the sequence {a_n} be a_ 1, a_2, a_3, ... If any given positive integer ε has a positive integer n, then when n >: when n holds | a _ n-l | < ε, then L is called the limit of the sequence {a_n}, which is recorded as.

lim┬(n∞)？ 「a_n = L」

This definition shows that when the number n of terms in a series approaches infinity, the value of the series will approach L infinitely. It can be understood that a position n is found in the sequence, and from this position, the gap between the value of the sequence and l can be controlled within the range of ε.

3. When understanding the definition of limit, we should pay attention to the following points:

Limit is a concept that describes the trend, and does not pay attention to the value of a function or sequence at a specific point.

The existence of a limit does not mean that a function or sequence is defined or converged at that point or at infinity.

The existence of limits does not guarantee uniqueness, that is, there may be many different limits.

By understanding these concepts, we can better understand and apply the definition of limit, and analyze and deduce it in mathematical problems.