Chapter 99： Teacher Xiao Zheng is starting the class

How terrible 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, but 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 even greater...

Because there was only one big class in advanced mathematics in the morning, it was only 9:35 when the class was over.

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 a championship uniform, walked along and asked Zheng Tianyu and Zhang Lei, "I didn't fully understand the proof question that the teacher just said. 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 also 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 don't think I 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 it, and began to explain it with excitement.

"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 00, f(1)=1-5+1=-3<0

According to the zero-point theorem, there is 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 proposition is proved! "

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, what a big deal, help each other, Lao Zheng, don't you think?" Zhang Lei smiled and squeezed his brows towards Zheng Tianyu.

Zheng Tianyu smiled, and the guy started to squeak again, but his 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 mobile 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 did not 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 perfect score in this semester, another roommate who had been silent all the time spoke up.

"Zhang Lei, that proves that lim{x→+∞}f\'(x)=lim{x→+∞}f\'\'(x)=0, wouldn't you?"

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

Seeing that the dormitory building was right in front of him, Zhang Lei's relaxed expression suddenly changed...

It's like constipation...

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

After organizing the language for a long time, he still didn't speak it.

[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 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. , he finally told the truth.

After the confession, Zhang Lei felt much more comfortable.

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

The other party's personality 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 from the sidelines, smiled and didn't speak. After all, no one asked about him, and what he said directly seemed to be a bit pretentious.

The group went straight back to the dormitory, followed by reading books and playing 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 have good grades, the others are average, and Shi Ze is the worst.

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

Then he turned his head, looked around the other four 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, you will miss it for life~"

"Ha? Isn't it the end of the due date, so why did the class start?" Shi Ze sat in 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 kitchens for these four people in the dormitory, which resulted in no one in the entire dormitory failing the exam.

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, tell us quickly, I'll get the whiteboard!" Zhang Lei quickly got off the bed with wide eyes, then quickly took out the whiteboard and hung it on the back of the dormitory door.

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

After doing all this, Zhang Lei smiled and said, "Mr. 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, the 5 people in the dormitory were sitting with chairs and watching.

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.

"A crime other than war..." Shi Ze scratched his head and sighed, mainly because Zhang Lei's last sentence reminded him.

He doesn't want to fail the exam. If he fails, he has to make up the exam. If he fails to take the exam, he has to retake it If he fails to retake the exam, he will not be able to graduate.

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

With this fantasy, Shi Ze was in high spirits, his back straightened in seconds, and his attention was 100% concentrated.

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

First, we can set lim{x→+∞}f(x)=C.

For any ε>0, when there is A>0 such that x>A |f(x)-C|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

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

Still by Lagrange's 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 good. 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!

​​