Chapter 137: No more checking, no problem
After sighing with emotion, Xu Qingzhou took a deep breath, picked up the pen and started writing slowly.
Question 1 is easy.
Question 2, no problem.
The penultimate question.
Let the function $f(x)=\sum_{n=1}^{\infty}\frac{\sin(nx)}{n^2+x^2}$, where $x\in\mathbb{R} $, it is not difficult to prove that $f(x)$ is in $\mathbb{R}$
. It involves series theory, function continuity, and the basic theorem of calculus. You can use the inequality $|\sin(nx)| \leq1$ and the convergence of the series \frac{1}{n^2+x^2}∑n=1∞ are done.
After 40 minutes passed, Xu Qingzhou put away his pen and took a sip of water, surrounded by the sound of Shasha's writing.
Next to him, Xu Zhengyang was grabbing his hair with a troubled expression on his face, Kong Xianbo was calculating, and there were already several pieces of manuscript paper piled up in front of him. Xue Ying and others also had particularly solemn expressions at this time.
In the distance, the old professor saw Xu Qingzhou looking around and coughed slightly, reminding Xu Qingzhou not to be clever.
Even though these professors are wearing reading glasses, your little move will tell you what your kid wants to do next.
For example, the boy drinking water is very suspicious.
Um?
However, as soon as he finished reminding him, he saw Xu Qingzhou picked up and walked towards the podium with a water glass and test paper.
The old professor was surprised: "Hand in the paper?"
"Yeah." Xu Qingzhou nodded.
Another mess
Next to me, a graduate student sighed. He was only in his freshman year and it was already messed up.
The graduate student was not surprised that Xu Qingzhou handed in the paper in half an hour. Even in the top universities, there are always one or two people who can fail.
The old professor obviously thinks so too. After teaching for decades, he has seen many such cases.
But
He just saw that this little guy seemed to be writing seriously?
Offstage.
Kong Xianbo and others, who were lowering their heads to do the questions seriously, also looked up blankly, handing in their papers? What paper should I hand in?
Lao Xu?
Damn it, it’s only been 40 minutes and this guy is done? !
Kong Xianbo expressed some confusion. Yes, he was mentally prepared. Lao Xu was definitely a strong opponent in professional classes, but... he didn't expect it to happen so quickly!
Liang Quanjie also raised his head and looked at Xu Qingzhou in astonishment as he walked up to the podium with the test papers.
So far, he has done half of it. He also read the test papers when they were handed out. There are two questions that are really difficult.
At least, until now, he has not thought of a suitable solution.
On the side, Xu Zhengyang gritted his teeth. He hadn't even finished half of it, and others had already handed in the paper? The gap between people has become so terrifying!
The old professor took the test paper with doubts and glanced at it.
oh? Full of writing?
"Don't you want to check?" the old professor asked.
"I won't check anymore." Xu Qingzhou shook his head and smiled shyly: "There is no problem, it should be correct."
After saying that, he smiled sheepishly, carrying his schoolbag, and leaving a cool figure behind everyone in the classroom who were gnashing their teeth.
Xu Qingzhou thought to himself: Hehe, let you feel my despair during the political exam.
No problem, damn, listen to what people say!
Under the stage, Xu Zhengyang and others cursed in their hearts at the same time.
Simple? The old professor smiled in his heart. This young man was quite arrogant. The questions asked by Lao Gu were so tricky, but someone actually said they were easy?
Shaking his head, he sat down on the podium, curiously picked up Xu Qingzhou's test paper, and looked at the name first.
Xu Qingzhou?
The old professor raised his eyebrows, as if he had heard of this young man. Oh, opposite, he is a student who has just entered the School of Mathematics. He has a very good talent and the paper he wrote is quite wonderful. If it were him
The old professor laughed dumbly. This freshman question was indeed difficult.
The old professor began to check Xu Qingzhou's test paper. He glanced at the simple questions in the front, then skipped them and looked directly at the last two big questions.
The first question. Well, that’s a good answer.
The old professor nodded slightly, which showed that this young man had a solid foundation in mathematics.
The last question is the most difficult.
The first question is a typical limit problem.
There is actually a trap here, because since the value of \ln(1+x)ln(1+x) at x=0 is 0, directly substituting it will cause the denominator to be 0. A more accurate treatment is to use Lópida's rule Or Taylor expansion to find the limit.
Yo, well done.
The old professor nodded again.
Indeed, Xu Qingzhou also discovered this trap when he was doing this question, and he sighed a little in his heart. Old Gu is too dark-hearted. He doesn't know how many people have fallen into this trap.
After calculating for a long time, I found out that it was wrong and I went crazy.
After 5 minutes, the old professor put down the test paper and exhaled. Yes, yes, the School of Mathematics really had a good idea.
After the exam, Xu Qingzhou went directly to the library and continued reading.
The exam times for the School of Mathematics and the School of Physics are staggered by several days. On the morning of the 5th, the last subject in the School of Mathematics is Advanced Algebra, while the School of Physics takes the general physics exam.
Xu Qingzhou was alone in the library. Song Yao had a professional course exam. At this time, he was busy reviewing for the professional course exam. In order to save time, he did not come to the library.
There was no one on the other side, and when he was too tired, he had no pretty face to look at, so he could only take out his mobile phone.
Not surprisingly, the circle of friends was in mourning.
Kong Xianbo: Ah, ah, mathematical analysis, I almost didn’t finish it. It’s over.
Xu Zhengyang: I would like to ask, if you take the make-up exam, what are your chances of passing it.
Then there are Zhai Ziqiang, Zhang Shuyi, Xue Ying and others
Perhaps it is because they have lived for a few more decades. Xu Qingzhou feels a little emotional, this is youth, able to vent freely, and the elderly, if they really encounter something, they will not be able to express themselves at all. Will not appear in the circle of friends.
Everyone's circle of friends is very interesting, using different words and emoticons to express that they did not do well in the exam.
Xu Qingzhou looked at it with great interest. After looking through it for a long time, he saw two words in the picture between the words - to be finished.
The questions that Professor Gu set this time were indeed difficult. I don’t know if it was because he wanted to kill these talented people, or if it was just a routine operation. Based on Xu Qingzhou’s understanding of Professor Gu, he probably favored the first type.
People like Xu Zhengyang were killed by mistake, and they have no spirit.
The day passed quickly. At 10:30 in the evening, Xu Qingzhou returned to the dormitory building with his schoolbag on his back.
The dormitory building is still the same as before. Advertisements from study abroad institutions are posted in the corridors. Which seniors and seniors have gone to Harvard, Stanford, and MIT? They are like countless warnings, telling students about the future they may miss—— When applying to a foreign school, every test score will be scrutinized.
Of course, when studying for graduate school in China, grade points are almost the only condition that determines eligibility for admission.
Glancing at the newly posted flyer, Xu Qingzhou shook his head and sighed, "Beijing University is full of troublemakers."
If he hadn't been a loser, he would probably have had to risk his life just like he did in his previous life.
When he returned to the dormitory, his roommates had also just returned. It had only been a day, and Xu Zhengyang's whole person had undergone a lot of changes, as if he had grown up in an instant. To be more precise, his face had a melancholy temperament.
(End of chapter)