1. Substitution method: Substitute a variable into a function to get a numerical value, which is the function value of this point.

2. Pinch Theorem: Through the pinch theorem, an upper and lower bound is found, which makes the upper and lower bound infinitely approach the target point, thus obtaining the limit value.

3. Four algorithms of limit: Use four algorithms of function limit to find the limit value.

4. Robida's Law: Convert the limit into the limit of the derivative of two functions, and then calculate.

5. Taylor formula: Use Taylor formula to expand the function and approximately express it as a polynomial, so as to find its limit.

6. Newton-Leibniz formula: Use Newton-Leibniz formula to calculate the limit value of the function at a certain point.

7. Parity and periodicity analysis method: through the characteristics of parity and periodicity, it is judged whether the function has a limit at a certain point.

Conditions for the existence of function limits

Function limit is one of the most basic concepts in higher mathematics, and the concepts such as derivative are all completed on the definition of function limit. Rational application of limit properties of functions. The common properties of function limit are uniqueness, local boundedness, order preservation, algorithm of function limit, composite function limit and so on.

There are two conditions for the existence of function limit:

1, the function tends to the target value: that is, when the independent variable tends to a certain value, the function value tends to a fixed value.

2. Uniqueness of approximation: when the independent variable approaches the target value, the function will eventually converge to the same value no matter which direction it approaches, otherwise the function limit does not exist.