Definition of 1. limit: Let the function f(x) be defined in a neighborhood of point A. If the independent variable x is infinitely close to a and the function f(x) is infinitely close to a certain number L, then L is called the limit of the function f(x) at point A, and it is denoted as LIMF (x) = L.
2. The nature of limit: including uniqueness, boundedness, number preservation and four algorithms.
3. Infinitely small quantity and infinitely large quantity: Infinitely small quantity refers to the quantity whose function value is infinitely close to 0 when the independent variable X is infinitely close to a certain point; Infinite quantity refers to the amount by which the function value increases or decreases infinitely when the independent variable x approaches a certain point infinitely.
4. Conditions for the existence of limit: there are two conditions for the existence of limit of a function at a certain point: first, the function is defined near this point; Second, the behavior of the function tends to a certain value near this point.
5. Calculation methods of limit: including direct method of substitution, pinch theorem, Lobida rule, Taylor formula, etc.
6. Limit of infinite series and infinite series: the limit of infinite series is that the elements in exponential series are infinitely close to a certain number; The limit of infinite series means that the partial sum of series is infinitely close to a certain number.
7. Limit of continuous function: If the limit of a function exists at a certain point, then the function is continuous at that point.
8. Geometric explanation of limit: On the two-dimensional plane, the limit of a function at a certain point can be regarded as the shortest distance between that point and the function image.
The above are some basic knowledge of mathematical limit, which is the basis of understanding and mastering calculus.