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Chapter 252: The Xueba Lecture has started!

Cheng Nuo Xueba Lecture has started!

What should I do if I can't solve the problems that I'm a bad student?
Mostly it's a fee!
Just have a bottle of Shenbao!
Cheng Nuo picked up two bottles of Kidney Treasure from the bookshelf, handed each of Zhao Yang and Li Peng a bottle, and then started his Xueba lecture hall mode.

Cheng Nuo had already seen the three questions that Zhao Yang couldn't do.

Judging from Cheng Nuo's experience in reading countless girls... Ah bah, reading countless questions, these three questions are more difficult than the general postgraduate entrance examination questions.

It's no wonder that Zhao Yang, who Cheng Nuo thought was good at mathematics, only solved two of the five questions.

"You really know how to do it?" Zhao Yang looked Cheng Nuo up and down suspiciously.

After more than a month of understanding Cheng Nuo's talent in mathematics, Zhao Yang already had a very deep understanding.

It can be said that it is definitely not an accident that Cheng Nuo was able to become the only person with a perfect score in mathematics in the college entrance examination.

So, when encountering a topic that he didn't understand, the first person Zhao Yang thought of was Cheng Nuo.

Can……

High talent belongs to high talent.

Zhao Yang still couldn't believe that Cheng Nuo had figured out the correct answer in less than 2 minutes for a question that he had been unable to solve for several hours.

Facing Zhao Yang's doubts, Cheng Nuo shrugged indifferently, "Whether I will do it or not, won't it be clear after listening to me?"

With a dubious attitude, Zhao Yang and Li Peng looked at each other and sat back beside Cheng Nuo again.

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

Cheng Nuo first talked about the third of the five exercises.

“求∫dx/x^4+1和∫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 on a different level.

The methods of exchanging elements, simplifying, making up points, and integrating by parts cannot solve this problem.

"I have used four or five integration methods for this problem, but none seem to be able to solve it smoothly." Zhao Yang frowned next to him and said, "I guess, I should use an alternative solution method, but how to do it specifically, How to write the formula, I haven't figured it out yet."

Cheng Nuo turned his pen, nodded and smiled, "You're right. This problem really cannot be solved with the four conventional solutions taught in class. Don't worry, it's hard to say whether the correct answer can be calculated in the end. "

"Then what calculation method should be used to solve this problem?" Li Peng, who had been silent all this time, asked curiously.

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

"Hua Luogeng's scoring method?" Obviously, both of them felt very unfamiliar with this term.

"Hua Luogeng's integral method is a combined integral method proposed by Mr. Hua Luogeng to solve integrals." Cheng Nuo explained, "Actually, it doesn't matter whether you know this integral method, as long as you know how to use it. Look..."

Cheng Nuo wrote down the specific calculation steps of this problem on the 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 formulas to get 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.

"Hey, this is the calculation process of Hua Luogeng's points. With this method of points, this problem is very simple." Cheng Nuo said very relaxed.

"For the rest, find that ∫dx/x^4+x^2+1, the reason is the same, you can just get it in the same way." Cheng Nuo didn't bother to calculate the second integral.

I told Zhao Yang the calculation method, if Zhao Yang still doesn't know how to calculate it, then just leave the group and forget it.

Zhao Yang nodded, "Well, I was the one who made this problem complicated before. But, speaking of which, Cheng Nuo, how did you know that this is called... Hua Luogeng's points?"

This is what Zhao Yang was curious about.

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

But why did Cheng Nuo know about Hua Luogeng's points, but he didn't understand anything.

Zhao Yang didn't remember that Teacher Shufen had taught this problem-solving theorem in class.

"Ah!" Cheng Nuo picked up the thermos cup on the table, took a sip, patted Zhao Yang on the shoulder, and said earnestly, "Student Zhao Yang, as students of Tsinghua University, we shouldn't just be satisfied with the teacher's presence." knowledge taught in the classroom.”

"The millions of books in the school library are not for you to watch from afar. You should use your extracurricular time to enrich yourself as much as possible!"

"Didn't you ask me how I know Hua Luogeng's integral?" Cheng Nuo said, taking down a copy of "Differential Mathematics and Its Applications" from the shelf, and put it in front of Zhao Yang, with a serious tone, "Chapter 3 of this book The fifth section is about Hua Luogeng's points."

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

And the title of that page is impressively—"The Nature of Geodesics in Differential Geometry"!
This has something to do with Temiao's Hua Luogeng points!
"Ahem..." Cheng Nuo coughed a few times, then smiled mischievously, "Misremembered, misremembered. Alright, let's skip this topic and look at the fourth question."

Cheng Nuo originally wanted to use this reason to preach, but now it seems that he has screwed up.

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

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

This question is not difficult for Cheng Nuo.

Basically, without too much thinking, swish, swish, swish, under the watchful eyes of Zhao Yang and Li Peng, Cheng Nuo wrote down his steps to solve the problem on the draft paper.

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

"f(x)=arctanx,..."

The calculation formula for this problem is a little more complicated.

But to Cheng Nuo, it was just a complicated calculation formula.

In less than 2 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 went straight to the fifth question.

It is still a matter of seeking the limit.

However, the required limit formula is very complicated, and it cannot be solved with any Lagrangian median theorem, L'Hopital's rule, clamping theorem, Taylor's formula or the like.

Cheng Nuo found another way, combining 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 a dozen formulas, Cheng Nuo easily solved the problem.

"Do you understand?" Cheng Nuo asked the two of them while putting the cap on his pen without looking up.

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

"Here, take it, take it back to the dormitory and read it slowly." After tearing it, Cheng Nuo tore off the page of the draft paper and stuffed it into Li Peng's hands.

Li Peng and Zhao Yang stood up, "Well, Cheng Nuo, thank you. Li Peng and I will leave first."

Cheng Nuo waved his hand, "You don't have to thank me, students, it's a duty to help each other."

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

Cheng Nuo smiled, "That's a good relationship."

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

As soon as the door to the dormitory was closed, Cheng Nuo quickly lay down on the computer table and shouted eagerly to the other three people in the dormitory, "Quick, start another round while there is still time. I don't believe in this round." Can’t eat chicken!”

…………

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(End of this chapter)