I Am the President of the University

How scary is +50% learning comprehension?

For example, when a teacher is explaining a topic, the number of topics that can be understood will vary according to each person’s understanding.

For example, student A can only understand 50 questions originally, but with a 50% comprehension bonus, he can increase his understanding from 50 questions to 75 questions.

And student B, originally could only understand 100 questions, but after the bonus, the questions that can be understood instantly become 150!

Originally, the gap between students A and B was 50 questions. After the addition, the gap between the two directly turned into 75 questions!

this means……

Smart people, after the bonus, will be smarter!

Thus, the distance from ordinary people is greater...

Because there is only one big class in high school in the morning, it is only 9:35 after the class.

Zheng Tianyu directly woke up the two sleeping roommates, and then the six people in the dormitory walked slowly on the way back.

At this point, there is no need to go to the cafeteria to queue up. Zheng Tianyu and his roommates discussed issues while walking along the road.

Except for the two sleeping, the other four listened carefully to the class.

Although Guanghua University is only a private second-class university, it will not degenerate so quickly as soon as you enter the school. Generally, they start to be bold when they are in their sophomore year, and become an old-fashioned dough stick when they reach their third year.

Zheng Tianyu and Zhang Lei understood everything, but the other two roommates were still a little confused.

Chen Chu, who was wearing the championship clothes, walked along the road and asked Zheng Tianyu and Zhang Lei, "I didn't fully understand the proof question that the teacher said just now. Can anyone of you understand it and explain it to me?"

"Which topic?" Zhang Lei was confident, and felt that he understood everything in today's lecture.

Although Zheng Tianyu didn't speak, he turned his attention.

"It's the proof that the equation x^5-5x+1=0 has one and only one positive root less than 1. I feel like I don't understand this question very well." Chen Chu frowned slightly when he spoke.

"This question, it's not difficult!" Zhang Lei just understood the question when he asked the question, and began to explain it with great enthusiasm.

"Just use the zero-point theorem.

Let f(x)=x^5-5x+1

Obviously, the function is continuous and derivable in the real number domain, we take the interval [0, 1]

f'(x)=5x^4-5=5(x^4-1)

When 0\u003cx\u003c1, f'(x)\u003c0, so f(x) is monotonically decreasing at (0, 1).

And because f(0)=1\u003e0, f(1)=1-5+1=-3\u003c0

According to the zero-point theorem, there exists ξ on (0, 1) such that f(ξ)=0.

And because it is monotonically decreasing, there is only one root such as ξ.

So the title is proven! "

After Zhang Lei finished speaking, Chen Chu had an epiphany and said gratefully: "Thank you, I understand now! I'll invite you to drink milk tea at noon later!"

"Hey, it's a big deal, help each other, Lao Zheng, don't you think?" Zhang Lei smiled, frowning towards Zheng Tianyu.

Zheng Tianyu smiled, and the guy started to squeak again, but the answer was indeed correct, so he replied:

"Yes, yes, that's right."

On the other hand, Shi Ze looked surprised. He stopped playing with his phone. After putting it away, he patted Zhang Lei on the shoulder and said, "Brother Zhang, hehe, copy the notes for me when you go back."

Zhang Lei didn't refuse, and readily agreed: "No problem!"

He's a good-looking guy, but he's a nice guy. There is nothing wrong with it other than pretending.

Just when Zhang Lei felt that he had achieved a high score this semester, another roommate who had been silent all the time spoke.

"Zhang Lei, that proves that lim{x→+∞} f'(x)=lim{x→+∞} f''(x)=0,

Would you not? "

"This question... um, I think about it."

Seeing that the dormitory building is in front of me, but Zhang Lei's relaxed expression suddenly changed...

like constipation...

He scratched his head, thought for a long time, and opened and closed his mouth.

Organized language for a long time, but still did not speak.

[It hurts, I can barely understand this question, how should I explain it? ! 】

Zhang Lei thought to himself, and suddenly became a little impatient.

And several roommates, except Zheng Tianyu, were all looking at him.

"This question...this question...cough, it's not very easy to explain, I, in fact, barely understand it, I'm sorry, Aaron." Zhang Lei hesitated again and again, blushing, and really couldn't explain this question. , and finally he told the truth.

After the confession, Zhang Lei felt much more comfortable.

The question was raised by Tao Yalun, the youngest in the dormitory, from Handong.

The character of the other party is just relatively quiet, not very talkative, and has a good personality.

Tao Yalun smiled slightly and said, "It's alright, I'll download it after I go back."

Zheng Tianyu, who was watching everything, smiled and didn't speak. After all, he didn't ask about himself, and what he said directly seemed to be a bit coercive.

The group went straight back to the dormitory, then read books, and played games, while Zheng Tianyu sat in front of his computer typing codes.

It's just that within half an hour of knocking, a voice came from behind.

"Tianyu, do you know the topic you just said? Can you tell me about it..."

Zheng Tianyu looked back, Tao Yalun was standing behind the chair and asked a little embarrassedly.

It's been a year since I came to Guanghua University. Among the 6 people in the dormitory, Zheng Tianyu and Zhang Lei performed better, the others were average, and Shi Ze was the worst.

"Yes, no problem." Zheng Tianyu replied with a smile.

Then he turned his head, looked around the other 4 people in the dormitory, and shouted loudly:

"Hey! Brothers, let go of what you are doing first. Teacher Xiao Zheng is starting the class~ Wait for a thousand years, and you will miss it for life~"

"Ha? Isn't it the end of the due date, why did the class start?" Shi Ze sat on the chair and called the glory of the king. When he heard Zheng Tianyu's words, he raised his head and asked in confusion.

There are 2.5 scumbags in the dormitory, Shi Ze contributed 1, and Chen Chu, Tao Yalun, and Liu Yi contributed 0.5.

At the end of the term, Zheng Tianyu and Zhang Lei took turns opening small stoves for these four people in the dormitory, which resulted in no one failing the class in the entire dormitory.

Tao Yalun replied to Shi Ze, "Just the question I asked on the way back to the dormitory."

"That proof question?" Zhang Lei, who was lying on the bed reading a book, rolled around and sat upright in an instant, and asked Zheng Tianyu, "Old Zheng, do you know that question?"

"Ang, I will, and it's not difficult." Zheng Tianyu replied easily.

"I'll wipe, it's true or not, then tell us quickly, I'll get the whiteboard!" Zhang Lei widened his eyes and quickly climbed off the bed, then quickly took out the whiteboard and hung it on the back of the dormitory door.

Then lock the door back so you don't have to worry about someone pushing it open.

After doing all this, Zhang Lei smiled and said, "Mr. Xiao Zheng, the whiteboard is ready, you can start the lecture."

"As for this question, then I'll give you a good talk." Zheng Tianyu stepped forward, picked up a pen, and began to write on the erasable whiteboard.

In the aisle in the middle of the dormitory, five people in the dormitory sat with chairs and watched.

Just as Zheng Tianyu turned his head and started to explain, he noticed that Shi Ze, who was sitting below, was still playing games with his head down.

He said directly: "Aze, stop playing games."

"That's right, Mr. Zheng, you still play games in class, do you want to fail the class?" Zhang Lei criticized Shi Ze sternly, grabbed the other party's mobile phone and put it on the table.

"Crimes of no war..." Shi Ze scratched his head and sighed, mainly because Zhang Lei's last sentence reminded him.

He didn't want to fail the course. If he failed the course, he had to make up the exam.

If you can't graduate...you have to get mixed doubles when you go home? ! !

With this fantasy, Shi Ze was full of energy, his back straightened in seconds, and his attention was 100% concentrated.

"How to prove lim{x→+∞} f'(x)=lim{x→+∞} f''(x)=0?

First, we can set lim{x→+∞} f(x)= C.

For any ε \u003e 0, there exists A \u003e 0 such that x \u003e A |f(x)-C|\u003cε/2, |f'''(x)|\u003cε/16.

For any x \u003e A, by the Lagrange mean value theorem, there exists b ∈ (x, x+2) such that f'(b)=(f(x+2)-f(x))/2.

Then |f'(b)|≤(|f(x+2)-C|+|f(x)-C|)/2 \u003cε.

Similarly, there exists c∈(x+6, x+8) such that |f'(c)|\u003cε.

Still by the Lagrange mean value theorem, there exists d∈(b,c) such that f''(d)=(f'(c)-f'(b))/(c-b)

 …”

ps: Ask for a recommendation ticket for a reward! There is only one chapter today... The remaining chapter will be added tomorrow! This Zheng Tianyu is an important figure. In the future, the main line will be scientific research + teaching, students are awesome, pretending + escorted by the principal, pretending to be forceful.

The principal's text is not very easy to write. I was sitting in front of the computer at 7 o'clock... Alas, I have been checking materials and making outlines.

Thanks to book friends "A Alaya Knowledge", "20200906145533199", "Two hundred catties of fat paper" for the rewards!