Cheng Nuo Xueba Lecture Hall has started!

I can't do the scumbag problem for a long time, what should I do?

Most of the time it's a fee!

Just have a bottle of kidney treasure!

Cheng Nuo picked up two bottles of kidney treasure from the bookshelf, handed one bottle to Zhao Yang and Li Peng, and then started his Xueba lecture hall mode.

The three questions that Zhao Yang can't do, Cheng Nuo has already seen them.

Cheng Nuo reads countless women...... Ah, from the experience of reading countless questions, these three questions are more difficult than the general postgraduate examination questions.

It's no wonder that Zhao Yang, a guy who Cheng Nuo thinks has a good level of mathematics, only made two out of five questions.

"Will you really do it?" Zhao Yang looked Cheng Nuo up and down with a suspicious gaze.

For Cheng Nuo's talent in mathematics, after more than a month of understanding, Zhao Yang has a very deep understanding.

It can be said that it is absolutely no accident that Cheng Nuo was able to become the only perfect score in mathematics in the college entrance examination.

Therefore, when he encountered a topic that he didn't know this time, the first person Zhao Yang thought of was Cheng Nuo.

Can......

High talent is high talent.

Zhao Yang still couldn't believe that the question that he couldn't solve for hours was in Cheng Nuo's hands, and it took less than two minutes to calculate the correct answer.

In the face of Zhao Yang's questioning, Cheng Nuo shrugged indifferently, "Will I do it, won't it be clear after listening to me once?"

With a half-believing mentality, Zhao Yang and Li Peng glanced at each other and sat back next to Cheng Nuo again.

Cheng Nuo smiled, took out a pen, brushed it a few times, and wrote the title on the scratch paper first.

Cheng Nuo first talked about the third of the five practice questions.

"Find ∫ dx/x^4+1 and ∫dx/x^4+x^2+1. ”

In terms of difficulty, this is the easiest of the three questions.

Compared with ordinary indefinite integrals, the difficulty is naturally not at the same level.

The methods of commuting, simplifying, making up points, and partial integrals cannot solve this problem.

"I used four or five integration methods for this problem, but I couldn't seem to solve it smoothly. Zhao Yang frowned beside him and said, "I guess it should be an alternative solution method, but I haven't figured out exactly how to do it and how to write the formula." ”

Cheng Nuo turned his pen, nodded and smiled, "You are right, this problem really cannot be solved by the four conventional solutions taught in class." Trouble aside, it's hard to say whether the correct answer can be calculated in the end. ”

"Then what kind of arithmetic method should be used to solve this problem?" Li Peng, who had been silent, asked curiously.

Cheng Nuo slowly spoke, "Hua Luogeng's integral method." ”

"Hua Luogeng's integral method?" Obviously, both of them are extremely unfamiliar with this term.

"Hua Luogeng's integral method is a combinatorial integral method proposed by Mr. Hua Luogeng for solving integrals. Cheng Nuo explained, "Actually, it doesn't matter if you know this integration method or not, as long as you can use it." You see......"

Cheng Nuo wrote the specific operation steps of this problem on scratch paper.

∫dx/x^4+1+∫x^2dx/x^4+1=∫(x^2+1)dx/x^4+1=∫d(x-x^-1)/(x-............

∫x^2dx/x^4+1-∫dx/x^4+1=∫............

Subtract the two equations to give the value of ∫dx/x^4+1.

Originally, Zhao Yang thought that the calculation steps were extremely complicated, but in Cheng Nuo's pen, they were just three simple formulas.

"Oh, this is the calculation process of Hua Luogeng's integral. With this integral method, the problem is very simple. Cheng Nuo said very relaxedly.

"For the rest∫ dx/x^4+x^2+1, the reason is the same, you just need to get the same directly. "Cheng Nuo didn't bother to calculate the second integral.

The calculation method has been told to Zhao Yang, if Zhao Yang still can't calculate it, then just leave the group.

Zhao Yang nodded, "Well, I really complicated this issue before. However, then again, Cheng Nuo, how do you know, this is called...... Hua Luogeng's points?"

This is where Zhao Yang is curious.

Same school, same teacher, same curriculum. Even Cheng Nuo skipped a class last week.

Why does Cheng Nuo know about this Hua Luogeng points, but he doesn't understand anything.

Zhao Yang doesn't remember that when the teacher was in class, he talked about this problem-solving theorem.

"Alas!" Cheng Nuo picked up the thermos cup on the table, took a sip, patted Zhao Yang's shoulder, and said earnestly, "Zhao Yang, as students of Tsinghua University, we should not be satisfied with the knowledge taught by the teacher in class. ”

"The millions of books in the school library are not for you to use from afar. I should use my extracurricular time to enrich myself as much as possible!"

"Didn't you ask me how I knew Hua Luogeng's integrals?" Cheng Nuo said, taking down a copy of "Differential Mathematics and Its Applications" on the bookshelf, and putting it in front of Zhao Yang, his tone was serious, "The fifth section of the third chapter of this book is about Hua Luogeng's integrals. ”

Zhao Yang took the book "Differential Mathematics and Its Applications" and turned to the page that Cheng Nuo said.

And the title of that page was "The Nature of Geodesics in Differential Geometry"!

This has a half-dime relationship with Temeow's Hua Luogeng points!

"Ahem...... Cheng Nuo coughed dryly a few times and smiled, "I remember wrong, I remember wrong." Okay, let's skip that topic and look at question four. ”

Cheng Nuo originally wanted to use this reason to preach, but now it seems that he has been messed up by himself.

Cheng Nuo took Zhao Yang's homework book and continued to talk about the fourth question.

"Finding the limit of the sequence l=lim(arctann+1/n-π/4)√n^2+n. ”

This topic is not very difficult for Cheng Nuo.

Basically, without thinking too much, under the gaze of Zhao Yang and Li Peng, Cheng Nuo wrote down his own steps to solve the problem on scratch paper.

“π/4=arctan1，arctann+1/n=arctan(1+1/n)”

“f(x)=arctanx，......”

The formula for this question is a little more complicated.

But for Cheng Nuo, it's just a complicated calculation formula.

In less than two minutes, Cheng Nuo had already written the last stroke.

“l=lim......=0.5。 ”

Ignoring the surprised gazes of the two people next to him, Cheng Nuo directly counted the fifth question.

It's still a matter of finding the limit.

However, it is very complicated to find the limit formula, and it is impossible to solve the Lagrange median value theorem, Lopida's law, clamping theorem, Taylor's formula or something.

Cheng Nuo found a different way and combined Cauchy's convergence theorem with Stolz's theorem.

“limf(x)/x^n+1=limf(x+h)-f(x)/(x+h)^n+1-x^n+1......”

After more than a dozen formulas, Cheng Nuo easily solved the problem.

"Do you understand?" Cheng Nuo didn't look up, and asked the two of them while putting on the cap of the pen.

"There are still a few formulas in the fifth question that I don't understand. Li Peng told the truth.

"Come, take it, take it back to the dormitory and take a look. Cheng Nuo tore off the page of the scratch paper and stuffed it into Li Peng's hand.

Li Peng and Zhao Yang got up, "Then Cheng Nuo, thank you, Li Peng and I will leave first." ”

Cheng Nuo waved his hand, "No thanks, classmates, it's right to help each other." ”

Zhao Yang nodded, "Then Cheng Nuo, if you encounter any trouble in the future, we will also try our best to help." ”

Cheng Nuo smiled, "That feeling is good." ”

After being polite to each other, Cheng Nuo watched Zhao Yang and the two leave the dormitory.

As soon as the dormitory door was closed, Cheng Nuo quickly lay on the computer desk and yelled eagerly at the other three people in the dormitory, "Quick, while there is still time, hurry up and start another game." In this game, I don't believe that I can't eat chicken!"

............

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