Chapter 137 No more checking, no problem After expressing his emotion, Xu Qingzhou took a deep breath, picked up the pen and began to write slowly. Question 1: Easy. Question 2 is no problem either. The second to last question. Suppose function $ f(x)=\sum_{n=1}^{\infty}\frac{\sin(nx)}{n^2 + x^2}$, where $ x \in \mathbb{R}$, prove that $ f(x$ is in $\mathbb{R}$ It is not difficult. It involves series theory, function continuity, and the fundamental theorem of calculus. It can be done using the inequality $|\sin(nx)|\leq 1 $ and the convergence of the series \frac{1}{n^2 + x^2}∑n=1∞. 40 minutes later, Xu Qingzhou put away his pen and drank a sip of water. The sound of writing could be heard all around him. Next to him, Xu Zhengyang was grabbing his hair, looking troubled. Kong Xianbo was calculating, with several sheets of manuscript paper piled in front of him. People like Xue Ying also had particularly serious expressions at this time. In the distance, the old professor saw Xu Qingzhou looking around and coughed lightly, reminding Xu Qingzhou not to be clever. Don’t be fooled by the fact that these professors are wearing reading glasses. Just by looking at one of your small movements, they can tell what you are going to do next.
For example, the boy who drank water was very suspicious. Ok? However, just after he gave the reminder, he saw Xu Qingzhou stand up and walk towards the podium with a water cup and test paper. The old professor was surprised: "Hand in the paper?" "Yeah." Xu Qingzhou nodded. Another lousy one. A graduate student next to him sighed and said, "He's only a freshman and he's already starting to give up." The graduate students were not surprised that Xu Qingzhou handed in the paper after 30 minutes. Even in the top universities, there are always one or two people who give up. The old professor obviously thinks so too. Having taught for decades, he has seen countless cases like this. But Just now he saw that this little guy seemed to be writing seriously? offstage. Kong Xianbo and others who were working on their papers looked up blankly. Hand in the papers? What papers? Lao Xu? Holy shit, it’s only been 40 minutes and this guy has already finished it?! Kong Xianbo was a little confused. Yes, he was mentally prepared that Lao Xu would definitely be a strong opponent in professional courses, but he didn't expect it to be so fast! Liang Quanjie also looked up and looked in astonishment at Xu Qingzhou who walked up to the podium with the test paper. So far, he has finished half of it. He also looked at the test paper when it was distributed and found that two questions were quite difficult. At least, up to now, he has not thought of a suitable solution. Xu Zhengyang was gritting his teeth as he watched. He hadn't even finished half of the work, but others had already handed in their papers? Has the gap between people become so terrifying? The old professor took the test paper with doubt and glanced at it. Oh? Full of words? "Don't you want to check?" asked the old professor. "I won't check it anymore." Xu Qingzhou shook his head and smiled shyly: "It's not difficult, it shouldn't be wrong." After saying that, he smiled embarrassedly again, carrying his schoolbag, and left a chic back to the people in the classroom who were gritting their teeth.
Xu Qingzhou thought to himself: Hehe, let me let you feel my despair during the political science exam. It’s not a difficult problem. Damn, listen to what human beings are saying! Below 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 is quite arrogant. The question asked by Lao Gu was so tricky. How could someone say it was simple? Shaking his head, he sat down on the podium, picked up Xu Qingzhou's test paper curiously, 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 new student in the School of Mathematics, very talented, and the paper he wrote is quite brilliant. If it is him The old professor burst out laughing. This question for freshmen is indeed not difficult. The old professor began to check Xu Qingzhou's test paper. He glanced at the simple questions at the beginning, skipped them, and looked directly at the last two big questions. Question 1. Well, you answered it well. 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 question. There is actually a trap here, because \ln(1+x)ln(1+x) has a value of 0 at x=0, so substituting it directly into the equation will result in a denominator of 0. A more precise approach is to use L'Hôpital's rule or Taylor expansion to find the limit. Yo, well handled. 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, thinking that Old Gu was too cruel. He didn't know how many people had fallen into this trap. After spending half a day calculating, I found out in the end that it was wrong, which made me crazy. After 5 minutes, the old professor put down the test paper and breathed a sigh of relief. Not bad, not bad, the School of Mathematics has indeed produced a good talent. After the exam, Xu Qingzhou went directly to the library and continued reading. The examination times of the School of Mathematics and the School of Physics are staggered by a few days. On the morning of the 5th, the School of Mathematics will take the last subject of advanced algebra, and the School of Physics will take the general physics exam. Xu Qingzhou was the only one in the library. Song Yao had a professional exam and was busy reviewing for it at the moment. In order to save time, she did not come to the library. There was one less person on the other side, and when he was tired there was no pretty face to look at, so he could only take out his cell phone. As expected, there was wailing among the friends circle. Kong Xianbo: Ahhh, mathematical analysis. I almost didn’t finish it. Finished. Xu Zhengyang: Please tell me, if I take the make-up exam, what are the chances of passing it. Then there are Zhai Ziqiang, Zhang Shuyi, Xue Ying and others Maybe it's because he has lived for a few decades longer, Xu Qingzhou feels a little emotional, this is what youth means, being able to vent freely. If older people really encounter something, they will not appear in the circle of friends at all. 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 flipping through it for a long time, he saw two words in the picture between the words - it's over. The questions Professor Gu asked this time were indeed difficult. I don't know if he wanted to dampen the spirits of these talented people or if it was simply a routine operation. Based on Xu Qingzhou's understanding of Professor Gu, he estimated that he was leaning towards the first option. People like Xu Zhengyang were killed by mistake. They had no fighting spirit.
The day passed quickly, and at 10: in the evening, Xu Qingzhou returned to the dormitory building with his schoolbag. The dormitory building remains the same as before, with advertisements of study-abroad agencies posted in the corridors, and which seniors went to Harvard, Stanford, or MIT. They are like countless warnings, telling students about the future they might miss out on - when applying to foreign schools, every test score will be examined. Of course, when studying for a master's degree in the country, GPA is almost the only condition that determines the eligibility for admission. After glancing at the newly posted flyer, Xu Qingzhou shook his head and sighed, Peking University is full of lottery kings. If he wasn't a cheater, he would probably have to risk his life just like in his previous life. When he returned to the dormitory, his roommates had just returned. In just one day, Xu Zhengyang looked much more mature, as if he had grown up in an instant. To be more precise, there was a hint of melancholy on his face. (End of this chapter)