1, using the continuity of the function to find the limit of the function. If it is an elementary function and the point is within the defined interval, then to calculate the limit at that time, just calculate the corresponding function value. Find the limit of function with organized numerator or denominator. If there is a root symbol, the method of removing the root symbol is generally adopted.
2. Find the limit of a function with two important limits. Using the property of infinitesimal to find the limit of function. Using L'H?pital's law to find the limit of function. Robida's law is a relatively simple and quick method for calculating the limit of indefinite sum type.
3. Replace the equivalent infinitesimal to find the limit of the function. In the process of finding the limit, sometimes the calculation process can be simplified by equivalent infinitesimal substitution. Find the limit of function by Taylor formula. For some complex functions, if they can be expanded into Taylor series, then the calculation process can be simplified by using the properties of Taylor series.
4. Find the limit of function by definite integral. For some limit problems related to definite integral, we can solve them by transforming them into definite integral problems and using the calculation method of definite integral. Using the relationship between derivative and limit to find the limit of function. In some cases, the limit problem of a function can be transformed into a derivative problem.
5. Determine the monotonicity and extreme value of the function by calculating the derivative, and then get the limit of the function. In advanced mathematics, finding the limit of function is a very important knowledge point, which requires us to master a variety of methods and skills. In the process of solving problems, we should choose appropriate methods and skills to solve them according to specific problems.
The knowledge about higher-order functions is as follows:
1, advanced function is one of the important contents in advanced mathematics, which mainly includes the concept, properties, graphs and extreme values of functions. First of all, the concept of function is the basis of higher function. Function refers to the correspondence between two data sets, which is expressed in the form of analytical formula or table.
2. In the higher function, the definition domain and value domain of the function are two groups of non-empty numbers, and the corresponding relationship can be arithmetic operation, power, root, etc. Secondly, the nature of function is the core of higher function. The properties of functions include parity, monotonicity, periodicity, maximum value and so on.