Siheyuan: After being reincarnated as a master's daughter

Qin Huairu gently closed her eyes, feeling as if her heart was being pressed down by a heavy stone. She was so tired that even speaking became a luxury. She turned around silently and slowly lay back on the familiar but slightly worn-out bed, as if the whole world was moving away from her at this moment.

Thoughts surged in her mind like a tide, one after another. The first thing that came into her sight was her late husband Jia Dongxu, the man who had been with her through thick and thin. Recalling the days they spent together, there were laughter and tears, but no matter what, it was an unforgettable time.

Then, Sha Zhu appeared in front of her. This kind-hearted but somewhat reckless man always lends a hand to her at critical moments. She couldn't help but wonder, if she had been more decisive and got together with Sha Zhu earlier, without giving Lin Ying any chance to take advantage of her, would her life be different now? Maybe they would live a plain but happy life.

However, when her thoughts drifted to Deputy Director Li, her mood became more complicated. This powerful man's tenderness towards her gave her a glimmer of hope to change the fate of her family. She couldn't help but imagine how her family's life would change dramatically if Deputy Director Li was really willing to abandon his wife and choose to spend the rest of his life with her? Maybe they could get rid of poverty and live a rich and worry-free life. But at the same time, the condemnation of morality and conscience followed her like a shadow, which made her fall into deep contradictions.

Qin Huairu secretly despised her own immoral behavior as a third party, but at the same time she deeply understood that if she left Deputy Director Li as her support, raising three children to adulthood would probably become an unsolvable problem.

Every night when everyone was asleep, she lay in bed tossing and turning, her heart full of contradictions and struggles. On the one hand, she felt ashamed and guilty for destroying other people's families; on the other hand, the pressure of life was like a heavy mountain that made her breathless, forcing her to rely on the material support provided by Deputy Director Li.

In fact, Qin Huairu didn’t really feel sorry for the mere 200 yuan.

You know, over the years, she has received a lot of money from Deputy Director Li. However, what makes her angry is her only son, Banggeng, who is not doing well.

This kid is already a grown-up, but he still does those sneaky, shady things, and he was caught this time! And considering his terrible academic performance, he probably has little hope of getting into a regular high school, let alone a vocational school.

It seems that when he reaches the legal age, he has no books to read and no formal job, and he will most likely be forcibly sent to the countryside as an educated youth to settle down.

It seems that we need to think of a way and ask Deputy Director Li to think of a solution. Can we arrange a formal job for him?

Qin Huairu was full of confidence thinking that she had handed over everything to Deputy Director Li, and that Deputy Director Li would definitely help her do it.

As she was thinking, Qin Huairu fell asleep in a daze.

,,,,,,

None of the three children disturbed their mother.

Xiaodang, Huaihua and grandma started cooking, mainly Xiaodang.

Banggeng couldn't stand the depressing atmosphere at home any longer. He frowned, and there seemed to be a burning fire in his heart. He stood up quickly, picked up a coat from the hanger, and wrapped it tightly around himself. Without any hesitation or even a word, he rushed out the door like a gust of wind and disappeared at the entrance of the alley in the blink of an eye.

This sudden scene startled Huaihua, who was helping to wash vegetables outside the house. She quickly put down her work and shouted in the direction where Banggeng left: "Brother, where are you going? The meal will be ready soon!" However, the only answer she got was the sound of footsteps in the distance and a figure gradually receding.

After a long while, Huaihua heard Banggeng's impatient voice coming from afar: "You eat your food and leave me alone! I'm going to my classmate's house to play!" After saying this, Banggeng's figure completely disappeared, leaving Huaihua standing alone at the door, staring blankly into the distance, her heart full of confusion and worry.

Jia Zhang also called out to Bang Geng, but Bang Geng ignored her.

At the same time, on the other side, at Yi Zhonghai's house.

Yi Jiale tightly grasped the two hundred-yuan bills, staring at them without blinking, her fingers nimbly turning them over, one after another, muttering something in her mouth, counting carefully. Her expression was focused and serious, as if the two hundred yuan were the most precious treasure in the world.

Yi Zhonghai, who was sitting next to him, slowly put down the teacup in his hand and looked at his daughter. Seeing her money-grubber look, he shook his head helplessly and sighed softly, "Tuanzi, Daddy has given you a lot of pocket money on weekdays, why are you still so money-grubber?"

However, Yi Jiale didn't even raise his head, and responded with muttered: "Hmph! Who would complain that their money is too little? Money makes the world go round, so it's never a bad idea to save more money!" After that, he continued to count the money, completely ignoring his father's words.

Yi Zhonghai was choked by his daughter's words and was speechless for a moment. He opened his mouth to refute, but finally chose to remain silent. He turned his head to look at his old wife who was busy beside him, and complained with a wry smile: "Look at our daughter, she is so obsessed with money, just like a miser. This character must be inherited from you!"

At this time, the aunt was squatting on the ground, concentrating on picking leeks, preparing to make a delicious leek and egg bun. Hearing her husband's words, she suddenly raised her head, put her hands on her waist, raised her eyebrows, and shouted in dissatisfaction: "Oh, what's wrong with liking money? This only shows that my daughter is smart and knows how to manage money! Besides, if my daughter doesn't take after me, will she take after someone else?"

Facing his wife's questioning, Yi Zhonghai suddenly felt short of breath. He smiled awkwardly, quickly picked up the teacup on the table, took a sip, trying to hide his embarrassment. Then he looked away as if nothing had happened, pretending that nothing had happened.

Okay, okay, he has always been the last one in this family, and he didn’t dare to say anything more and make the mother and daughter unhappy.

Yi Jiale counted the money for a while, then put the receipt and the money into the system space. He left a message to prevent villains like the Jia family.

…………

In the system space, Yi Jiale is learning sophomore knowledge with a virtual teacher.

As the teacher's lecture fell.

Yi Jiale stretched and said, "007, let's take the test!"

"Okay!" 007's cheerful childish voice sounded.

Then the books that had just been studied on the table disappeared, the teacher disappeared, and the knowledge points that the teacher had just explained on the big screen in front also disappeared.

A test paper appeared on the pure white table.

Yi Jiale picked up the test paper carefully and started doing the questions.

The previous multiple-choice questions, connecting questions, and fill-in-the-blank questions were relatively easy for Yijia Le, but the last big question was more difficult.

Question 1:

设函数 f(x)f(x) 在 [0, +\infty)[0,+∞) 上连续，且 f(x) \geq 0f(x)≥0，\int_{0}{+\infty} f(x) \, dx = 1∫

0

+∞f(x)dx=1. Proof:

\lim_{{x \to +\infty}} f(x) = 0lim

x→+∞

f(x)=0;

There exists x_0 \in [0, +\infty)x

0

∈[0,+∞), such that f(x_0) ＞ 0f(x

0

)＞0.

?answer?:

?Prove that \lim_{{x \to +\infty}} f(x) = 0lim

x→+∞

f(x)=0?:

Assume \lim_{{x \to +\infty}} f(x) \neq 0lim

x→+∞

f (x)

=0, then there exists some positive number M > 0M > 0 and a sufficiently large x_0x

0

, so that when x ＞ x_0x＞x

0

When , f(x) ＞ Mf(x)＞M.

由于 f(x) \geq 0f(x)≥0，我们可以得到 \int_{x_0}{+\infty} f(x) \, dx ＞ \int_{x_0}{+\infty} M \, dx = M(+\infty - x_0) = +\infty∫

x

0

+∞f(x)dx＞∫

x

0

+∞Mdx=M(+∞?x

0

)=+∞.

This is consistent with the given \int_{0}{+\infty} f(x) \, dx = 1∫

0

+∞f(x)dx=1 Contradiction. Therefore, the assumption does not hold, so \lim_{{x \to +\infty}} f(x) = 0lim

x→+∞

f(x)=0.

?Prove that there exists x_0 \in [0, +\infty)x

0

∈[0,+∞), such that f(x_0) ＞ 0f(x

0

)＞0?：

Assume that for all x \in [0, +\infty)x∈[0,+∞), f(x) = 0f(x)=0.

Then, \int_{0}{+\infty} f(x) \, dx = \int_{0}{+\infty} 0 \, dx = 0∫

0

+∞f(x)dx=∫

0

+∞0dx=0.

This is also consistent with the given \int_{0}{+\infty} f(x) \, dx = 1∫

0

+∞f(x)dx=1 Contradiction. Therefore, the assumption does not hold, so there exists x_0 \in [0, +\infty)x

0

∈[0,+∞), such that f(x_0) ＞ 0f(x

0

)＞0.

After answering the last two questions, Yi Jiale clicked the green button on the table to agree to hand in the paper.

As the test paper disappeared, the score appeared on the big screen in front of him.

100 points.

Yi Jiale breathed a sigh of relief. As expected, he got full marks again.

007: "Congratulations to the host for receiving another 500 full score bonus points and 5 IQ points."

"Host, where do you plan to add your IQ points?"

007 calls up the host's panel.

Host: Yi Jiale

Nickname: Tuanzi

Race: Human (Han)

Gender, age: Female, 8 years old

Memory (200): 160

Thinking ability: 200): 135

Observation (200): 135

Attention (200): 137

Imagination (200): 132

Average Intelligence: 139.8 (Excellent Intelligence 120-140)

Yi Jiale thought about it and decided to add it to his thinking ability. Now that he has learned university courses, he feels that if his thinking is not enough, his brain will not be enough. However, his imagination is a bit of a drag. Imagination is still very helpful for writing essays. Then Yi Jiale said:

"007, I've decided, +3 points for thinking ability, and +2 points for imagination."

"Okay, host."

Host: Yi Jiale

Nickname: Tuanzi

Race: Human (Han)

Gender, age: Female, 8 years old

Memory (200): 160

Thinking ability: 200): 138

Observation (200): 135

Attention (200): 137

Imagination (200): 133

Average Intelligence: 140.6 (average genius intelligence 140_160)

As 007's intelligence points were continuously added, colorful virtual fireworks suddenly bloomed in the sky, shining like the bright stars in the night sky. At the same time, 007's passionate and energetic voice rang out like a bell: "Congratulations! Congratulations! Dear host, you have finally successfully crossed the threshold to the realm of genius!"

Yi Jiale stared at the average intelligence value displayed on the screen in front of her with great joy, and saw a label following the number - "ordinary genius". Although it was only an ordinary genius, it was already a remarkable achievement for her. After all, she had officially entered the ranks of geniuses!

At this moment, Yi Jiale felt that her mind was clearer than ever before, as if all the knowledge and inspiration could flow into her mind in an instant. This wonderful feeling made her sigh: "Sure enough, the world of geniuses is completely different from that of ordinary people like us!"

"Hahaha, from now on I am also a genius..." Yi Jiale was immersed in extreme excitement and couldn't help laughing out loud. However, this joy did not last long. Just when she was getting carried away, she suddenly felt someone gently shaking her body.

007 said hurriedly: "Host, your father is asking you to get up and go to school, hurry back to reality!"

Then Yi Jiale woke up without saying a word.

Yi Jiale smiled and slowly opened his pair of eyes that were as bright as stars, looked at his father with joy, and asked in a tender voice: "Dad, please take a closer look at me. Is there any difference between me today and before?"

(Author: Finally added to this, something happened at home yesterday, I was in bad luck all night, and I came back late at night. As expected, it is not suitable to go out these two days, everything is not going well. I hope everyone can understand!!)