1. Infinity and Infinity: Infinity and Infinity are the basis of the concept of limit, but it may take some time and practice to understand their essence and nature. Especially for the comparison and operation of infinitesimal, we need to master some skills and methods.
2. Properties and theorems of limit: Limit has many important properties and theorems, such as pinch theorem, uniqueness of limit, four operations of limit and so on. The understanding and application of these properties and theorems require certain logical thinking and reasoning ability.
3. Limit of function: The limit of function is the core content of limit knowledge, but the limit of some functions may be complicated. For example, the limit of piecewise function, the limit of composite function, the limit of trigonometric function and so on. The limits of these functions need to be solved by analyzing the properties and structures of functions and applying the properties and theorems of limits.
4. Proof of limit existence: Sometimes it is necessary to prove that a function has a limit at a certain point, or that the limits of two functions are equal at a certain point. This requires the use of the properties and theorems of limit, combined with the properties of sequence or function for reasoning and proof.
5. Application of limit: Limit is widely used in mathematics, such as derivative, integral, series, etc. When learning these applications, we need to combine the concept and method of limit with other mathematical knowledge to understand and master the principles and ideas behind it.
In a word, extreme knowledge in senior high school mathematics is a complex and abstract concept, which requires students to have a certain mathematical foundation and thinking ability. Through continuous study and practice, we can gradually master the concept, nature and application of limit, so as to better understand and apply the knowledge of limit in mathematics.
Observing Objects is a difficult course in the fifth grade of primary school mathematics. So