1. Determine the type of limit: First, we need to determine the type of limit, whether it is series limit, function limit or infinite limit. Different types of restrictions have different solutions.
2. Simplify the expression: Before solving the limit, we need to simplify the expression, eliminate the zero factor in the denominator, and merge similar terms. In order to facilitate the subsequent solution.
3. Using the known limit properties: In the process of finding the limit, we can use the known limit properties, such as limit addition, subtraction, multiplication and division, compound function limit, pinch theorem and so on, to simplify the solution process.
4. Judging whether the limit exists: In some cases, we need to judge whether the limit we want exists. For example, when the function tends to different values on the left and right sides of a point, the limit of the point does not exist.
5. Using L'H?pital's Law: When we encounter an infinitive in the form of "0/0" or "∞/∞", we can use L'H?pital's Law to solve it. L'H?pital's law is a derivative method, which can be transformed into a known limit form.
6. Using Taylor expansion: When you encounter a limit that cannot be solved directly, you can try to approximate the function to a polynomial near a certain point by using Taylor expansion, thus simplifying the solution process.
7. Drawing aided analysis: For some complicated limit problems, we can draw aided analysis. For example, drawing a function image and observing the trend of the function near a certain point will help us understand the meaning of limit.
8. Summarize the law: When solving a series of similar limit problems, it is necessary to summarize the law and summarize the general solving methods. In this way, when we encounter new problems, we can find solutions quickly.
In a word, the analysis of mathematical limit problem needs to use various methods and skills flexibly, and solve it step by step by simplifying the expression, using known properties and judging the existence of limit. At the same time, do more exercises, sum up the rules and improve your problem-solving ability.