Chapter 287

[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)?]

In this calculation problem, Cheng Nuo set the problem solving point on the edge sub method.

A fifth-order nonsingular matrix is constructed according to the conditions given in the problem, and then it can be easily solved by using the epiedge method.

It's just that Professor Liao doesn't seem to have mentioned the knowledge point of the edge method in class.

Forget it, let them derive this theorem on their own, it shouldn't be that difficult.

Thinking like this, Cheng Nuo made a decision.

Left, there are still three big questions left.

Binary generation problems of polynomial rings, septal root problems of polynomials, equivalence problems to systems of stepped linear equations.

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

After checking it, Cheng Nuo didn't find any mistakes.

Cheng Nuo exhaled lightly and sandwiched the seven questions he came out into the test paper.

At this point, his work has been completed. And it took only one morning.

Cheng Nuo did not delay, and came to Professor Liao's office after lunch.

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

Professor Liao seemed to be busy with other things, and after receiving the test paper handed by Cheng Nuo, he just glanced at it a few times before handing it back to Cheng Nuo's hand again. "Give me a run, send this test paper to the Education and Science Office, and ask them to make 125 copies for the advanced generation exam of the Mathematics College. ”

"No problem, Professor, I'll go first?"

"Well, go ahead. ”

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

Cheng Nuo, who was busy with his work, returned to the dormitory.

Maddie was alone in the dorm. Seeing Cheng Nuo coming back, Maddie couldn't help but ask curiously, "Cheng Nuo, what did you do just now, I just heard a classmate say that he saw you coming out of it at the door of the Education Office?"

Cheng Nuo shrugged, "It's hard to say! In half a month, you will know what's going on." ”

Maddie: "Oh. ”

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

Final exams are approaching.

Cheng Nuocai remembered that he also served as a member of the study committee of the Department of Finance.

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

When it comes to university, self-consciousness is the most important thing, but if someone is there to supervise you a little, your motivation to study will increase a lot.

Since they are the only class in the finance department this year, there is nothing to compare in terms of grades.

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

But having said that, in the first semester of their freshman year of finance, in addition to advanced mathematics, the remaining courses are difficult to fail even if they start to review a week before the start of the exam.

Compared with some majors that "as long as you choose a good major, you will win the college entrance examination at the end of the year", and often take more than ten subjects, the students of their finance department are quite happy in the first two academic years.

As time passed, the entire Tsinghua campus was gradually enveloped in the atmosphere of final exams.

Seats in the library are rarely full.

The students on the road are also in a hurry, or directly holding a book and reviewing it on the school bench.

The solemn atmosphere is no less than the last few days before the college entrance examination.

By the 16th week of the fall semester, almost all faculties had been closed.

The torturous exam week has finally begun!

On January 15, Cheng Nuo's first subject was opened.

College English, a subject that Cheng Nuo thinks he can easily handle.

Holding a radio, a card pen, an ID card and a few other items, Cheng Nuo strode into the examination room. Confident and fearless!

His first exams at university will begin here.

Goal, Grand Scholarship!Come on!!

Cheng Nuo's condition is very good. As soon as he encounters the exam, he can make Cheng Nuo's whole person secrete a large amount of adrenaline hormones, as if he has been injected with chicken blood.

Forty-five minutes later......

Less than thirty seconds after the listening broadcast on the radio, everyone in the examination room saw a figure take off the headphones, stand up from his seat, pack up the test papers, walk to the front podium, and hand the answer sheet and answer sheet to a female invigilator. (Half an hour before the college English test is the writing time, and the listening will start after half an hour)

"Teacher, I'm done. ”

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

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

That guy...... This speed is really strong!

However, they were not disrupted by Cheng Nuo's speed. The final exam is to look at the results of the test papers, and there is a speed of submission of the papers.

Some bigwig-level academic tyrants obviously have the strength to hand in the papers half an hour early, but they try to be as stable as possible for higher scores. After all, at their level, one or two points is the difference between having a scholarship and not having a scholarship.

But Cheng Nuo doesn't care. Even if he was asked to check there for more than an hour, he couldn't find any errors. Because...... There are no mistakes on his test papers!

For Cheng Nuo, a man who pursues speed in everything, uh...... Except, of course, that thing! For him, time savings are a little.

Exams can be submitted in advance. It's like high school, and you have to sit bored for more than an hour when you're done.

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

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

I applied for exemption from listening from Professor Lu, so I have hardly been to the high math course since then, and I don't know anything about the knowledge points of the exam, the practice of exercises, etc. But that didn't affect his determination to get a perfect score.

One is for the special scholarship, and the other is for Cheng Nuo to continue to prepare for the application for exemption from high mathematics classes next semester. If you don't pass the high math score this time, then you won't have the face to go to Professor Lu to sign.

As soon as he got the high math test paper, Cheng Nuo first swept the questions from beginning to end.

Easy difficulty, okay!

The difficulty of the questions is basically within Cheng Nuo's expected range.

Cheng Nuo pulled out the cap of the pen and began to do the questions, first filling in the blanks with ten questions.

[The domain of the function y=arcsin√1-x^2+1/√1+x^2 is _______]

[Tangent equation from the function y=e^2+x (1,0)_______]

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

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

Whew!

The questions are very simple, and it is even easier for Cheng Nuo, who has already taken courses in the mathematics department.

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

[Let f(x) have a continuous reciprocal on [a,b], f(a)=f(b)=0, and ............]

The solution is to prove that f(x) is actually a Γ function through the infinite anomalous integral of f(x) in the range of the interval [a,b], and then use the balance element formula of the Γ function to solve it.