1. Calculus: Limit is one of the basic concepts of calculus. Through limits, we can define derivatives and integrals, and use them to solve various problems, such as the extreme value of a function, the tangent of a curve, the area under a curve and so on.
2. Series: The limit formula can be used to judge the convergence of series. Series is a series of infinite terms, and whether the series converges to a certain value can be judged by the limit.
3. Function approximation: The limit formula can be used to describe the approximation behavior of a function. When a complex function is expressed as an infinite series, the limit can be used to estimate the value of the function at a certain point or to calculate the average value of the function in a certain interval.
4. Probability theory: Limit formula also has important applications in probability theory. For example, the probability density function of binomial distribution can be calculated by limit.
5. Statistics: Limit formula is used to calculate the asymptotic properties of sample mean and variance in statistics. By using the limit, we can deduce the relationship between the sample mean and variance and the population mean and variance.
6. Numerical analysis: Limit formula is used to solve equations and optimization problems in numerical analysis. By discretizing the continuous problem and approaching the continuous solution with the limit, the practical problem can be solved by numerical method.
In a word, the limit formula is widely used in the field of mathematics, which provides a powerful tool for us to solve various mathematical problems.