Chapter 70: Lagrange remainder
Chapter 70
Shen Yue was purely too lazy to use her brain. She just wanted to enjoy the feeling of being cared for when Qing Xiaoyu explained the problems to her. As for Jiang Shiwen, he tried his best to understand but really could not comprehend it.
Qing Xiaoyu looked at the time and started rushing people. "Afternoon classes are about to start. Aren\'t you guys leaving yet?"
When Zou Xuerong saw the time, she immediately panicked. Today was her first day of school and she could not be late. Luckily, her classroom was right next door.
"I\'ll go first then. Yueyue, I\'ll come find you after school..." After saying this, Zou Xuerong softly said to Qing Xiaoyu again, "Thank you too."
Qing Xiaoyu politely replied, "You\'re welcome."
Jiang Shiwen was extremely frustrated, but still left with Zou Xuerong.
His grades in class were usually average to below average, and the teachers never called on him, so he had a decent self-image.
But today, getting taught how to solve problems by someone younger than him, and still not understanding after listening, this was truly unbearable!
He didn\'t have to study, but if he did study and still didn\'t understand, that was unacceptable!
Jiang Shiwen secretly made up his mind to start working hard in his studies from today. At least next time, he would be able to understand.
Niu Kaihuai walked into the classroom for his first afternoon class of math, and the first thing he saw was the awake Shen Yue. His eyebrows raised in surprise.
Niu Kaihuai believed he was never someone to sacrifice himself, if he wanted to know something then he would definitely find out. So he directly asked Shen Yue, "How come you\'re not sleeping?"
Shen Yue: ?
Seeing that Shen Yue did not respond, Niu Kaihuai thought she didn\'t hear clearly, so he asked again, "Why aren\'t you sleeping today?"
Shen Yue confirmed he was talking to her before replying, "So I can sleep well tonight."
Hearing this answer, Niu Kaihuai actually felt it was quite reasonable, but also not that reasonable.
Looking at Shen Yue\'s peaceful face, Niu Kaihuai directly wrote a question on the blackboard and said to Shen Yue, "Shen Yue, come up and solve this question before class starts. If you can\'t solve it, you\'ll have to stand for the whole class."
Let\'s see if you\'re really awake or pretending, Old Niu thought.
The question on the blackboard was very simple, prove:
tan1>3/2.
This was a very standard proof question, but for ordinary lower year high school students who had only learned some basic formulas, it was no doubt beyond their level.
Ye Yin took one look and wondered if Shen Yue had offended Teacher Niu, otherwise why would he ask her such a question?
To solve this question using conventional methods would require first drawing the tangent line to y=tanx at x=π/3.
Then use f(x) to hypothetically take the derivative, and prove it is monotonically decreasing over the domain, in order to prove tan1>3/2.
There were only 5 minutes left until class started. If one was not already very familiar with the knowledge required to solve this type of problem and proficient at it, it would be impossible to finish solving it in 5 minutes.
Ye Yin couldn\'t help but sweat a little for Shen Yue.
However, if Shen Yue could not solve this problem, then maybe he could take the opportunity while explaining the solution to talk to her.
No no no, that was the wrong mindset! How could he have such malicious thoughts, wishing for a classmate to be unable to solve the problem!
Although it was true probably only a few students in the class could solve this problem conventionally, he still could not curse Shen Yue.
Ye Yin started chanting scriptures, while Shen Yue looking at the problem on the board, only had that sentence in her mind - if you can\'t solve it, you\'ll stand for the whole class.
Stand for the whole class.
The whole class standing, too tiring, no way, absolutely no way.
She was only 12 years old, right at the age where she should not think about anything nor do anything, just quietly accumulate energy in preparation for prison in the future. How could she waste time standing!
She must sit!!
At this moment, a surge of fighting spirit suddenly welled up in Shen Yue\'s heart, the determination to absolutely not stand for a whole class.
She went up to the lectern, picked up a piece of chalk, glanced at the question twice, and started searching her brain for relevant knowledge points.
Learn as you go and understand as you learn.
Shen Yue held the chalk and paused for about a minute without moving. Niu Kaihuai\'s heart gradually sank.
Damn, don\'t tell me this girl really can\'t solve it? If he really did make her stand for the whole class, wouldn\'t Shen Ge stew him into soup?!
It was all because Shen Ge had insisted Shen Yue was a math genius, misleading him. If only Shen Ge hadn\'t said such words that day, he would not have come up with such an overly difficult question!
No matter, even if Shen Yue couldn\'t solve it, he could just say later that he intentionally used this problem to stimulate the class, no big deal.
As Niu Kaihuai reassured himself, Shen Yue finally started writing.
From the first stroke to the end, it was done in one go without any pause, taking less than one minute. She had solved the problem completely.
Well, not solved, written out the solution.
It was as if the answer was already in her heart, she had just written out the answer in her heart.
When Shen Yue finished writing the solution, the bell for class had not rung yet.
Niu Kaihuai looked at Shen Yue\'s solution, surprised that she had not used the conventional derivative method, but rather used the inequality derived from Taylor\'s Formula to scale it.
If this question was solved using the normal method, it would take 5-6 lines of equations with repeated calculations. But now, in Shen Yue\'s hands, it was solved in just 3 equations.
Niu Kaihuai stared at Shen Yue\'s solution, checking it over and over before finally confirming it was correct.
When he turned his head, he saw Shen Yue looking obediently at him, her eyes clearly asking, Can I go back to my seat now?
Niu Kaihuai had a feeling he had grasped something, but the feeling flashed by in an instant, and he was unable to hold onto it. He could only wave his hand to let Shen Yue return to her seat.
Shen Yue let out a long breath as she sat down.
Phew, no need to stand.
At this time, Qing Xiaoyu squeezed over and looked at Shen Yue with eyes completely different from the morning, full of astonishment. "Shen Yue, you can even use Taylor\'s Formula? I only just learned this formula from Ye Yin yesterday."
Shen Yue nodded, she had also learned it yesterday.
She had accidentally overheard it being taught next door while sleeping, and conveniently committed it to memory. She just now felt it might be useful and dug out the knowledge to mull it over in her head. She didn\'t expect to really be able to solve the problem with it.
However, even if she couldn\'t solve it that way, there was another method she could use, just a bit slower. She likely wouldn\'t have been able to finish writing it before the class bell rang, so she would\'ve had to stand.
Luckily, there was a Taylor\'s Formula in her brain.
Although she didn\'t know who had told her about it...she was grateful for nature\'s gift.
Seeing Shen Yue\'s little act of putting her hands together in prayer, Qing Xiaoyu curiously leaned in and asked, "What are you doing?"
Shen Yue\'s actions unchanged, "I\'m thanking nature for its gifts."
Qing Xiaoyu: ?
Although she didn\'t really understand, it was so cute.
Qing Xiaoyu poked the back of Shen Yue\'s hand. "Class is starting, Teacher Niu is looking at you."
"I\'m too tired, I need to rest."
Qing Xiaoyu and Shen Yue were sitting in the second row, loudly scheming. The aching Niu Kaihuai could hear everything. Finally unable to endure it, he said, "Shen Yue, you just solved one problem and you\'re tired already? Come up and solve another one. If you can solve it you can mess around however you want this class, if not then pay attention!"
Niu Kaihuai gave a calculus problem, fully confident.
5 minutes later...
"Go ahead and play...keep it lowkey, don\'t tell your brother."
And so Shen Yue very openly started reading a novel.
One Birth 108 Treasures, The Great President is Very Troubled.