1. Describe the changing trend of the function: Limit can help us understand the behavior of the function near a certain point, so as to better understand the properties and characteristics of the function. For example, we can use limits to study the continuity, differentiability and monotonicity of functions.
2. Calculate the function value: By calculating the limit, the value of the function at a certain point can be calculated, which is very important for solving practical problems. For example, in physics, we often need to calculate the speed or acceleration of an object at a certain point.
3. Derivation formula: Limit also plays an important role in the derivation of mathematical formula. For example, Taylor formula is a method to approximate the solution of complex function through limit. In addition, some important limit theorems, such as L 'Bida Law and Pinch Theorem, are also based on the concept of limit.
4. Establish calculus theory: Limit is the basis of calculus theory. Calculus mainly includes differential calculus and integral calculus, both of which are defined and deduced by limit. For example, the derivative is the tangent slope of the function at a certain point, and the integral is the area under the function curve.
5. Solving practical problems: Limit also plays an important role in solving practical problems. For example, in economics, we often need to calculate marginal costs and marginal benefits; In biology, we need to consider the population growth rate and so on. These problems can be solved by limits.
In a word, limit plays an important role in mathematical analysis, which provides a powerful tool for us to study the properties of functions, calculate their values, derive formulas, establish calculus theory and solve practical problems.