1. Definition of limit: In mathematics, a limit is the value of a function at or near a certain point. If the limit of a function exists at a certain point, then we say that the function is continuous at that point.
2. The nature of limit: limit has uniqueness, boundedness, sign preservation and four operational properties.
3. Calculation method of limit: The calculation of limit mainly includes direct method of substitution, pinch theorem, Lobida rule, infinitesimal method of substitution, etc.
4. Infinitely small quantity and infinitely large quantity: Infinitely small quantity refers to the quantity whose function value is infinitely close to zero when the independent variable is infinitely close to a certain point; Infinity refers to the amount by which the function value increases or decreases when the independent variable approaches a certain point infinitely.
5. Continuity of limit: If the limit of a function exists at a certain point, then the function is continuous at that point. On the other hand, if a function is continuous at a certain point, then the limit of this function at that point also exists.
6. Convergence of limit: If the terms of a series are getting closer to a certain number, then we say that the series is convergent. On the other hand, if the terms of a series are farther and farther away from a certain number, then we say that the series is divergent.
7. Existence of limit: If both the left limit and the right limit of a function exist and are equal at a certain point, then we say that the limit of this function exists at that point.
The above are some basic knowledge about limit in college mathematics, and it is very important to understand and master these knowledge for learning more advanced mathematics courses.