1. Intuitive understanding: limit can be understood as the "trend" of a sequence or function at a certain point or at infinity. For example, when x approaches 0, the value of sin(x) fluctuates between-1 and 1, which is the limit of sin(x) when x=0.
2. Definition of limit: In mathematics, we usually use ε-δ (ε-δ) language to define limit. For a function f(x), if there is a positive number δ for any given positive number ε, so that when |x-a|.
3. The nature of limit: limit has many important properties, such as uniqueness, boundedness, sign preservation and so on. These properties provide convenience for us to understand and calculate the limit.
4. Calculation of limit: In practical problems, we often need to calculate the limit of a function. This usually requires some basic limit formulas and techniques, such as L'H?pital's law, pinch theorem and so on.
5. Relationship between limit and continuity: In the real number field, if a function has a limit at a certain point, then the function is continuous at this point. So limit is a necessary condition for continuity.
Generally speaking, understanding the limit needs to combine intuitive understanding, strict definition, property analysis, calculation method and continuity. Only by fully understanding these aspects can we truly grasp the important concept of limit.