From small town scholar to chief scientist

Chapter 52 This is Operations Research

At this moment, the whole examination hall was silent.
Originally, students who had done a lot of real questions and listened to many teachers' lectures did not write at all.

It's all about who I am, where I am, and why I'm entering a math competition.

Why are these math problems different from the previous ones, and why are they so much more difficult.

Even the first question, many people can't understand the question.

There are six big questions in the whole test paper.
Questions 20, [-], and [-] and [-] are worth [-] points, and questions [-] and [-] are worth [-] points.

Generally speaking, students in the examination room only need to solve one question to win the prize, the third prize at the municipal level.

That's right, you only need to solve one question to win the prize.

This is what Professor Tang Ping mentioned in class.

It is conceivable how difficult the topics of the mathematics competition are.

Compared with the practice questions, it is harder than the real questions of the mathematics major entrance examination, and it is more difficult than the so-called counting one, two, three.

Coupled with the fact that there are many bigwigs participating in the competition this year, the questioner's hands trembled again, and the questions were much more difficult than in previous years.

At this moment, Li Xiaodong, the seventh-ranked top student in class one, was holding the paper and looking at the first question.

First question title:
【Assume that S is an ellipsoid in the three-dimensional Euclidean space, P is a fixed point in the space, and P is not on S.

For any X ∈ S , denote that X* is the midpoint of the line segment PX.Question: What is the trajectory of all such points X*?Justify your conclusion. 】

After reading it, I couldn't help but sigh, oh my god, these are some fairy topics,
Why can't I understand the meaning of some questions?
Am I really a math major?
Am I really good at math?
Am I really suitable for this major?

Even the title of the first question has no clue.

A lot of people scold their mothers with the title, the ghost knows what track you are on.

I won't do this question, the next one.

I do not believe the next question I will not!

Generally speaking, analytic geometry is the best score, and it is also the simplest. If you can't get a score for this topic, it means that you will miss the award in this competition with a high probability.

Of course, it is not ruled out that those who have learned well in the high-level scores can get points from the high-level questions.

In the silent examination room at this moment, only Zhou Yi who is in the middle writes with a pen, dare to come up with this kind of question?
No need to think about the first big question, instant kill!

This time I didn't think about Zhouyi, I don't know how to cook!
Zhou Yi let out a crazy cry in his heart.

After writing hundreds of pages of papers and reading so many books, there is no need to think about it. Every time I think about it, Zhou Yi realizes that he has not yet reached the realm of teleportation, and he is still a dish.

But today, I, Zhou Yi, can finally make a cry,
I don't need to think, I don't cook!
The whole table was matched with a signature pen, and there was a burst of noise,

Zhou Yi wrote directly:

[Assume that the equation of the ellipsoid in the O-xyz Cartesian coordinate system is x/a+y/b+z/c=1,

newline,

Set point P=(α, β, γ), then for any X ={x, y, z}∈ S, the meaning of the question is

X*=1/2(X+P).;

Therefore, it can be seen that the surface figure formed by X* is an ellipsoid whose center point is {α/2, β/2, γ/2 )}. 】

Not long after, the first answer was written down by Zhou Yiyang eloquently.

Zhou Yi looked at the neat rolled noodles, without a trace of stain, and immediately felt that it was perfect.

so easy!

The students in the entire examination room panicked when they heard the sound of Zhou Yi writing.
Doesn't this boss need to think about it?

Brother Zhou, do you know that every time you write, the sound you make, and the answers you write are not answers to the test papers, but tortures to my soul.

Why am I such a dish?
In the same school, in the same mathematics college, taught by the same teacher, and with the same scores, why is there such a big gap between Yuda?

The key test paper didn't even give multiple-choice questions, and didn't even give me a chance for metaphysics.

After Zhou Yi finished writing, he stopped writing, and everyone breathed a sigh of relief when they heard that Zhou Yi was not writing.

Fortunately, it seems that the topic is still difficult, at least the boss of Zhouyi stopped writing and thinking.

Otherwise it would be too unreasonable.

Zhou Yi stopped writing just because he started to read the title of the second question, not thinking.

The second question is a question of calculating points, which is a question in a score.

【∫0到+∞（x-x+x^3-x^4-x^2018）/(x+1)^2021dx。】

After reading Zhou Yi, the thoughts in his mind took shape instantly, without thinking for a second.

write directly,

[It is easy to know that I_k=∫0 to +∞, x^k/(1+x)^2021dx converges, so we can set x=1/t
From the linear operation of the integral, the integral is zero. 】

At this time, the sound of Zhou Yi writing pen made another sound appear in the silent examination room. Every sound seemed to be as heavy as a thousand weights, hitting the hearts of 29 candidates hard.

After writing the Book of Changes, continue to read the third answer question,

A high-generation topic, still kills in seconds,

No difficulty.

The fourth question is still an algebra-oriented question, without difficulty, instant kill.

For four questions in a row, except for the interval when reading the questions, Zhou Yi hardly stopped writing.

Until the fifth question, analyze the questions inside together.

At this time, the students in the examination room breathed a sigh of relief.

Now the time for you to stop writing in Zhouyi can finally be delayed to more than 10 seconds,

Thank goodness this made me realize that I'm not a piece of shit.

Everyone guessed it by staying for three seconds before. It is estimated that Zhou Shen was reading the topic, so he stopped writing.

What does it mean if it stays for more than ten seconds now?
It shows that Zhou God also has questions to think about!

The topic of the fifth question should also be considered by the academic master.
What does it mean to think about it?
means dish!
I think therefore I cook, the truth that has been handed down forever in the Department of Mathematics.

So: I = dish,
Zhou God = dish,
Deduced: I = God of Zhou!

Perfect logic, I am worthy of being a leader in mathematics.

The reason why Zhou Yi stayed for more than ten seconds was not thinking, but that there were two ways of thinking that instantly appeared in his mind, indicating that there were two ways to solve the problem, so which one should he write?

Each has its advantages, why don't we just write two of them?

What if it is considered a violation for me, but there are two ways not to write it up, and I am not allowed to pretend, I am so uncomfortable.

After debating for a while, Zhou Yi still decided to write the one with less writing on the blackboard.
[Assuming that the upper and lower limits are L and l respectively, then s<l<L<1, according to the recursive formula,., so it can be proved that the limit exists, and the limit is equal to 2021^(1/2021). 】

After finishing writing, Zhou Yi let out a long sigh,

Ugh.

It's a pity that I dare not take the risk of writing two solutions, otherwise I will write both of them.

The second solution requires more writing on the blackboard and uses more methods.
First of all, the first step is to use mathematical induction. After deriving the derivation, use the monotone bounded convergence theorem.

It is concluded that the convergence is 1, and finally the jia, b theorem has to be used.

There are so many mathematical things used in it, and the amount of calculation is too large, it is really not worthwhile, wasting my refills.

A pen refill costs one yuan. Wouldn't it be nice to buy a meat bun for this one yuan?

Zhou Yi immediately decided that he would eat a meat bun for lunch as a reward for his wit.

It is very operational research to exchange the least money for the highest score, get the biggest reward, and get the strongest glory.

(End of this chapter)