First, the origin and development of extreme ideas
As early as in ancient China, the connotation of limit thought was used. In China, Liu Hui, a mathematician, used the idea of limit when he developed three pi rapidly. His "Circumcision" is the best proof of modern extreme thoughts and the earliest record of China's extreme thoughts. With the passage of time and the continuous development of materials, more and more scholars began to come into contact with extreme thoughts, and many representatives of early extreme thoughts emerged, such as Zhuangzi. But in the early days, the idea of limit was not directly defined, but only applied to its connotation. With the continuous progress of science, the concept of limit was not put forward until Newton's time. However, due to the limitations of the times, the concept of limit in that period was not scientific. At that time, the research on limit thought was mainly carried out through the analysis of infinitesimal quantity, but because of the great defects in the research foundation, the results obtained were also flawed. The development prospect of things is bright, but the road must be tortuous. Because of this, the development of extreme ideas has also experienced many controversies, including the idea of trying to avoid using extreme ideas through other solutions, but all ended in failure. The most rigorous definition of limit thought is Wells Trust, who defined limit in ε-δ language and solved many mathematical problems at that time. Today, extreme thoughts can be seen everywhere in advanced mathematics, but students still know nothing about the relationship between extreme thoughts and our daily economic life. Therefore, this paper mainly analyzes the application of extreme thinking in economic life.
Second, the application and analysis of limit in economic life
In order to improve students' understanding of extreme thoughts in higher vocational colleges, this paper will use case analysis to explain the extreme thoughts embodied in life.
1. Heritage Department
Before a farmer died, he took his 19 cows as his inheritance and distributed them to the eldest, the second and the third in turn according to the proportion of one-half, one-quarter and one-fifth, but it was clearly stated in his will that the cows could not be slaughtered and sold. In order to distribute the farmer's inheritance according to his will, the three brothers have no way to start. Later, they had to let their neighbors borrow a cow to share the farmer's property. Finally, the three brothers got ten, five and four heads respectively. This treatment reflects the application of extreme thoughts in life. According to the farmers' wishes, the three brothers will always share the cows without borrowing them, because the sum of the proportions is not equal to 1, only 19/20. Without the idea of limit, this problem cannot be solved. According to the general algorithm, assuming that it needs to be divided into n times, the calculation process is as follows, where n- 1 is greater than or equal to 0:
The boss's cow =
Number of cows won by the second child =
The number of cows won by the third child =
According to this calculation method, no matter how many times it is divided in the end, there will still be cows left, so it is impossible to fulfill the wishes of farmers through this calculation. But if we apply the idea of limit, we will find that the above formula is a convergent infinite series, and the sum of the convergent infinite series = limx→ x0 (a1+a1q+a1q 2+). This example illustrates the important role of extreme thinking in solving life problems.
2. Garbage disposal problem
With the continuous development of economy and the continuous improvement of people's living standards, there are more and more domestic garbage and industrial garbage. At present, under the call of environmental protection, it is still a problem to deal with garbage scientifically, and the main problem to be solved now is at what speed. The limit idea is of great significance to the calculation of garbage disposal speed.
Take the garbage disposal in a city as an example. According to the statistical data of a city in 20 16, by the end of 20 16, the city's garbage has reached one million tons. According to the calculation, from 20 17, it is estimated that the city will produce nearly 50,000 tons of garbage every year, and 20% of the garbage left over from the previous year will be treated every year.
Limn→∞an=25 (ten thousand tons) can be calculated according to the limit and the related contents of the sequence.
According to the calculation, the processing speed of the city can't finish the garbage in time, and the remaining garbage will remain at 250,000 tons. Cities can discuss the scientific implementation of their policies or measures through calculation before formulating relevant policies or measures.
Third, the conclusion
Through the above research, we can find that extreme thoughts not only appear in advanced mathematics, but also have a close relationship with our lives. Using extreme thoughts can solve difficult problems in life. Based on this, students in higher vocational colleges should change their learning attitude and actively study how to use extreme thinking to solve problems. As a high school student, I have already felt the influence of extreme thoughts on economic life. In order to master and use extreme thoughts accurately, I will improve my learning ability through the following four aspects, that is, to lay a good foundation by mastering mathematical concepts and methods, to solve practical problems with mathematical knowledge and to innovate. What needs to be clear is that any knowledge has its inevitability of existence. Only by mastering knowledge can the corresponding mathematical ideas be applied to economic life. At first, students in higher vocational colleges will have obstacles in understanding extreme thoughts. At this time, students and teachers need to work together, students should study hard, and teachers should make the course teaching lively and interesting. Only in this way can we improve students' ability to learn economic mathematics well, thus promoting their ability to solve problems by using economic mathematics ideas.