1. Direct substitution method: When the limit of a function exists at a certain point, the value of that point can be directly substituted into the function expression for calculation.
2. Pinch theorem: When the limit of a function at a certain point cannot be directly calculated, we can find two functions so that their limit at this point is equal to the limit of the objective function at that point, and the values of these two functions near this point are less than or equal to the value of the objective function. According to the pinch theorem, the limit of the objective function at this point is equal to the average of the limits of these two functions at this point.
3. Robida's Law: When the limit form of a function at a certain point is "0/0" or "∞/∞", it can be solved by taking derivatives of the numerator and denominator respectively and then finding the limit.
4. Infinitesimal substitution method: When the limit form of a function at a certain point is "0/0" or "∞/∞", the infinitesimal is replaced by the value of the objective function value near that point, and then the limit can be solved.
5. Taylor expansion method: when the value of a function near a certain point can be expanded by Taylor series, the value of the function near that point can be approximately calculated by taking the first few terms of Taylor series, and then the limit can be calculated.
6. Using the properties of known limit: When the limit of one function at a certain point is equal to the limit of another known function at that point, it can be solved by using the properties of known limit.
These methods are only a part of the common methods to find the limit in higher mathematics, and there are actually many other methods that can be used to solve the limit problem. Different methods are suitable for different situations, and choosing the appropriate method can improve the efficiency and accuracy of the solution.