universal data

Chapter 284 As long as you choose your major well, you can win the college entrance examination at the end of every year!
287 chapter

[Known A^(-1)=(25,..., f(x)= A15 + xA25 + x^2A35 + x^3A45 + x^4A55
= A15 + xA25 + x^2A35 - x^3M45 + x^4A55, find the coefficient of -x^3 in f(x)? 】

For this calculation problem, Cheng Nuo set the point of breaking the problem on the method of adding edges.

Construct a fifth-order non-singular matrix through the conditions given in the title, and then use the edge-adding method to easily solve it.

It's just that Professor Liao didn't seem to mention the knowledge point of Jiabianzi method in class.

Forget it, let them derive this theorem by themselves, it shouldn't be too difficult.

With that in mind, Cheng Nuo made a final decision.

There are still three big questions left.

The problem of binary generation of polynomial rings, the problem of alternate roots of polynomials, and the equivalence problem of echelon-shaped linear equations.

Cheng Nuo came up with three questions based on these three key points.

After checking it, Cheng Nuo found no errors.

Cheng Nuo let out a breath, and put the seven questions he had asked into the test paper.

So far, all his work on the topic has been completed.And it took only one morning.

Cheng Nuo didn't delay at all, and came to Professor Liao's office after lunch.

"Teacher, I've finished writing the questions!" Cheng Nuo handed the final printed test paper to Professor Liao.

Professor Liao seemed to be busy with other things. He took the test paper from Cheng Nuo, glanced at it briefly, and handed it back to Cheng Nuo again. "Please do a favor for me and send this test paper to the Office of Education and Science, and ask them to make 125 copies for the high-level examination in the School of Mathematics."

"No problem, professor, then I'll go first?"

"Well, let's go."

…………

After finishing his work, Cheng Nuo returned to the dormitory.

Maddie was the only one in the dormitory.Seeing Cheng Nuo coming back, Maddie couldn't help but curiously asked, "Cheng Nuo, what did you do just now? I just heard a classmate say that he saw you coming out of the door of the Educational Science Office?"

Cheng Nuo shrugged, "It's hard to say! After half a month, you will know what happened."

Maddie: "Oh."

…………

Final exams approaching.

Cheng Nuo just remembered that he was still serving as a study committee member of the Finance Department.

Under the supervision of Squad Leader Yan, Cheng Nuo organized the students in the class to start evening self-study work.

Although when it comes to university, self-awareness is the most important thing, but if someone supervises you a little bit, your motivation to study will improve a lot.

Since there is only one class of them in the freshman Department of Finance this year, there is nothing to compare their grades.

Therefore, the goal of Cheng Nuo, the study committee member, is to ensure that there will be no students who fail in their class this semester.

But having said that, in addition to advanced mathematics, it is difficult to fail the remaining courses in the first semester of their finance department even if they start reviewing one week before the exam starts.

Compared with some majors where "as long as you choose your major well, you can win the college entrance examination at the end of each semester" and often take more than ten subjects, students in their finance department were quite happy in the first two academic years.

As time went by, the entire Tsinghua campus was gradually shrouded in the atmosphere of final exams.

The seats in the library are rarely full.

The students on the road were also in a hurry, or they just took a book and reviewed it on the school bench.

The dignified atmosphere was no less than the last few days before the college entrance examination.

In the 16th week of the autumn semester, almost all colleges have suspended classes.

The grueling exam week has finally begun!
On January 1th, Cheng Nuo's first subject exam started.

College English, a subject that Cheng Nuo thought he could handle easily.

Holding the radio, card marker pen, ID card and other items, Cheng Nuo strode into the examination room.Be confident and fearless!
His first university exam will begin here.

Goal, special scholarship!bring it on! !

Cheng Nuo was doing very well.As soon as he meets an exam, Cheng Nuo's whole body will be secreted with adrenaline, as if he has been injected with chicken blood.

45 minutes later...

Less than 30 seconds after the listening playback on the radio ended, everyone in the examination room saw a figure take off the earphones, stood up from the seat, packed up the test papers, walked to the front podium, and handed the answer sheets and answer cards to a person. A female invigilator. (The writing time is half an hour before the college English test, and the listening comprehension will start half an hour later)
"Teacher, I'm done."

Cheng Nuo's voice was not loud, but it was extremely clear in the silent examination room.

In the examination room, a person looked at Cheng Nuo at the podium in disbelief.

That guy... at this speed, he is really strong!

However, they were not disrupted by Cheng Nuo's swift handing in of the papers.The final exam is to look at the results of the test papers, and whether to look at the speed of handing in the papers.

Some top-level academic figures clearly have the ability to submit papers half an hour in advance, but they try their best to be stable for the sake of higher scores.After all, at their level, one point or two points is the difference between having a scholarship and not having a scholarship.

But Cheng Nuo didn't care.Even if he was asked to check there for more than an hour, he couldn't find any mistakes.Because... there were no mistakes in his test paper!

For Cheng Nuo, a man who pursues speed in everything, uh... Of course, except for that matter!For him, saving a little time is a little bit.

College is great!Exams can be submitted in advance.It's not like high school, where you have to sit around in boredom for more than an hour after you've finished everything.

…………

Two days later, Cheng Nuo ushered in his advanced mathematics exam.

I applied for a waiver from Professor Lu, so since then Nuo has almost never been to advanced mathematics courses. Cheng Nuo doesn't know anything about the exam knowledge points or exercises.But this did not affect his determination to get full marks.

One is for the special scholarship, and the other is because Cheng Nuo will continue to prepare for the waiver application for advanced mathematics next semester.If the high math scores are not enough this time, then there is no shame in going to Professor Lu to sign it.

The first time he got the high math test paper, Cheng Nuo scanned the questions from beginning to end.

Easy difficulty, okay!

The difficulty of the questions was basically within Cheng Nuo's expectations.

Cheng Nuo took off the cap of his pen and started to work on the questions, first filling in the blanks with ten questions.

【函数y=arcsin√1-x^2+1/√1+x^2的定义域为_______】

[The tangent equation from the point (2, 1) on the function y=e^0+x_______】

[Let f(x) be derivable at x0, and...]

…………

Swish swish!
The questions were very simple, especially for Cheng Nuo who had already taken courses in the mathematics department.

The only thing that is a little bit difficult is the last big question.

【Assume that f(x) has a continuous reciprocal on [a, b], f(a)=f(b)=0, and………】

The idea of ​​solving the problem is to use the infinite anomalous integral of f(x) in the interval [a, b] to prove that f(x) is actually a Γ function, and then use the residual formula of the Γ function to solve it.

(End of this chapter)