Definition of 1. limit: the limit of function f at point A means that when x is infinitely close to A, the value of f(x) is infinitely close to a certain number L, which we usually express as lim _ {x->; a}f(x)=L .
2. The nature of limit: limit has some basic properties, such as uniqueness, boundedness, and number preservation. These properties help us to understand and calculate the limit.
3. Existence of limits: Not all functions have limits. For example, the function f(x)= 1/x has no limit at x=0, because x cannot be equal to 0.
4. Four algorithms of limit: If we have two functions F and G, their limits of sum, difference, product and quotient (when denominator is not zero) are equal to their respective limits.
5. Limit of composite function: If function G maps function F to a new function, the limit of composite function f(g(x)) is equal to the limit of f multiplied by the limit of g. ..
6. Infinity and infinity: infinity and infinity are special cases of limit. Infinitesimal means that when X is infinitely close to A, f(x) is infinitely close to 0; Infinity means that when X is infinitely close to A, f(x) is infinitely close to positive infinity or negative infinity.
7. Calculation method of limit: There are many calculation methods of limit, including direct method of substitution, pinch theorem and L'H?pital's law.
8. Limit of continuous function: If a function is continuous at a certain point, its limit at that point is the function value at that point.
The above are some main knowledge points about limit, and understanding these knowledge points is very important for learning and understanding more advanced mathematical concepts.