From Almighty Scholar to Chief Scientist

Chapter 5 Leisure in Exams
"Okay, students, please bring your schoolbags and books up now, we will hand out the papers right away."

In the first examination room, the invigilator greeted the thirty students present.

At a glance, it can be found that this seems to be in the first class of science, because most of the students in this examination room are students in the first class of science, that is, students in the rocket class.

The examination rooms of Jincheng Middle School are sorted according to the rankings of the previous examination. There are [-] people in one examination room, so the top [-] people in the last examination can sit in the first examination room. It is also nicknamed the Battlefield of Xueba by the students of the school. , People from other examination rooms want to come in, but people here don't want to go out.

Lin Xiao sits in the fifth and last row, the second seat, which means he was ranked 2th in the last exam.

And behind him is Chen Ang, who was ranked 27th in the last exam.

After putting the schoolbag on the podium, before the teacher handed out the papers, they chatted a few words.

Chen Ang pointed to the first column, and asked, "Old Lin, are you going to attack the sequence of gods this time?"

The first column in the examination room is what they call the sequence of gods, that is, the top six in the grade, who are regarded as the gods of learning. Of course, the top six will change every time the exam is over, and the competition is still fierce. A small number of one or two can live in the top few.

Lin Xiao rolled his eyes: "Ah, yes, yes, how do you know?"

Chen Ang: "Look at your state for more than half a month, Jiang Jie can't learn from you."

"It's the third year of high school. If you don't work hard, you will go to the construction site in the future?"

"You are quite conscious."

"Stop talking, the exam is coming soon." Lin Xiao waved his hand, too lazy to talk to him.

Chen Ang prayed: "Don't test "Pipa Xing" when writing ancient poems silently."

The simulated exam is naturally the form of the college entrance examination. The first Chinese exam takes two and a half hours.

For this, Lin Xiao has nothing to do, the linguistic system does not recognize it.

So he can only write honestly based on what he has learned before.

However, when writing ancient poems silently, it was a coincidence that a sentence in "Pipa Xing" "the silver bottle broke and the water burst out, and the iron cavalry protruded and the sword and gun blared", Lin Xiao could even hear Chen Ang's voice coming from behind C language.

There is nothing to say about Chinese, as far as Lin Xiao can play normally.

Soon it was mathematics in the afternoon, which was the main meal for Lin Xiao.

After getting the test paper, he briefly browsed all the questions. He has basically mastered all the knowledge points of high school mathematics in the past half month, and quickly came to a conclusion.

150 points, steady.

He couldn't find any question that could make him lose his train of thought.

Whether it's the big questions behind, or the next few difficult questions that you choose to fill in the blanks.

Then, he started to write.

As he wrote, he even found that he hadn't entered that immersive state.

This is probably because his brain is too lazy to concentrate on thinking about this kind of problem.

Because whether he has entered the immersion state or not, the speed of solving this problem is the same, just like playing minesweeper with a GTX1080TI, the fan does not turn.

So just like that, he almost blocked and killed functions with functions, and wrote all the questions geometrically.

After finishing writing, he looked at the clock hanging in the classroom. Good guy, it's only been an hour, which means he finished this paper an hour earlier.

In the past, he definitely couldn't do this.

This made him feel a kind of blissful helplessness, because the examination room only allowed to hand in the papers half an hour earlier, and if he finished writing an hour earlier, he would have to wait honestly for half an hour.

Turning to look at the people around, well, they are all still working hard.

He shook his head, simply picked up the scratch paper, wrote the Taylor median theorem he had just learned some time ago, and began to try to deduce the proof method of this theorem.

Taylor's mean value theorem is one of the basic theorems in differential calculus, and plays an important role in the mean value theorem of differential calculus.

And the best way to understand a theorem is to learn how to prove it.

Therefore, Lin Xiao is now trying to prove it with the methods he can think of.

As for what method to use?

He fell into thinking, his knowledge reserve was limited to high school and junior high school, and he didn't have many proof tools, and he didn't want to use the methods he knew before to prove, such as using Cauchy's median theorem or L'Hopital's rule, etc. .

After all, for him, this is like a challenge in his spare time, and he has to go out of his own way.

It's probably like walking on the sidewalk, looking at the bricks below, and challenging yourself not to step on the white ones.

Not for anything else, just for the joy of the mood.

Ever since, doing the test paper did not let him fall into the immersion state, and at this time he fell into it because of thinking about this problem.

Not long after, his eyes suddenly lit up, and he found an idea.

That is to use mathematical induction, which is one of the few proof methods he has mastered in high school.

When you have an idea, start writing.

He quickly turned over the draft paper, which was blank.

In fact, after finishing the test paper, he didn't use much on the first side of the draft paper, because he solved the answers directly on the answer sheet, and some questions were calculated by mental calculation. .

Without saying much, he started writing from the top.

[Taylor's mean value theorem: If the function f(x) has a derivative up to (n+1) order in an open interval (a, b) containing x, then when x is in (a, b), f(x) It can be expressed as the sum of an n-degree polynomial of (x-x) and a remainder R(x): f (x)= f(x0)+ f′(x0)(x-x0)+...]

[Lemma 1: f(x) is derivable on [a, b], and f ′(x)≥0, then f(x)≥f(a), x∈[a, b].
Proof: Since f′(x)≥0, so...

Let g(x)...

build function h(x)...

Prove using mathematical induction for n:

If n=0, obviously established;
...]

It is also a challenge for Lin Xiao to prove such a problem for the first time, but this cannot prevent him from being quick enough in thinking.

Just like that, he wrote in a hurry, thinking about the advanced mathematics knowledge he had learned recently, as well as the knowledge that can be used in high school mathematics.

In addition to increasing his learning efficiency, the system has also improved his memory. Although it is not possible to achieve a photographic memory, he will not forget the knowledge he has learned so easily.

Those mathematical knowledge are like abstract concepts. You don't need to remember the detailed words, you only need to remember what it says in general, and then, when you use it, you can directly associate with the relevant knowledge.

Time passed slowly, and Lin Xiao looked like other students from the outside, immersed in the math papers.

An invigilator suddenly stepped down from the podium and began to inspect.

The invigilator is Ding Ping, a mathematics teacher, and he is also the teacher who trains Jiang Jie's students participating in the mathematics league.

As a national special-grade teacher, his attainments in mathematics are quite high, at least for high school mathematics, he is basically completely thorough.

(End of this chapter)