Xueba, I beg you to go and escort him quickly!

topic:

The known function f(x)=e(x power)+e(-x power) where e is the base of natural logarithm.

(1) Proof: f(x) is an even function on R;

(2) If the inequality mf(x)≤e(-x power)+m-1 holds true on (0, +∞) about x, find the value range of the real number m;

（3）已知正数a满足：存在x0∈[1,+∞)，使得f（x0）＜a（x03+3x0）成立，试比较e（a-1）次方与a（e-1）次方的大小，并证明结论。

When Xu Heng saw this question, he couldn't help feeling a little regretful.

. . . 0

"I kind of want to take this monthly exam."

Yue Pingting said, "You have no chance!"

Xu Heng smiled, "What is your train of thought?"

Yue Pingting said directly, "For the first question, I'll take -x, so I can prove it!"

Xu Heng, "Well, it mainly depends on the second question."

Yue Pingting, "I probably wrote the process, and the third question is the same, I will send it to you."

Send it with the picture.

Xu Heng took a rough look.

(2) According to the meaning of the question, m (e (-x power) + e (x power)) ≤ e (-x power) = m-1, that is...

……

……

If and only if t=2, the equal sign holds

So m≤-1/3.

Yue Pingting, "The third question, I use Guidance, I don't know if it works well!"

"Because you told me about seeking guidance before, but I think this third question is obviously beyond the outline..."

Xu Heng hit the nail on the head, "The reason for the existence of this third little question is to open the score line. There are only a few people who can do it, or even fewer people."

Xu Heng said while watching Yue Pingting's problem-solving process.

Again monotonically increasing, monotonically decreasing, and so on.

Very complicated.

……

Yue Pingting, "When I was solving the problem, I was afraid that I might make mistakes in the e, m, and a!"

After Xu Heng finished reading, "That's right! You can get full marks for this question."

With Xu Heng's affirmation, Yue Pingting heaved a long sigh of relief.

"Then I think I can get full marks in math..."

"Xu Heng, it's good to have you!"

Full score!

Speaking from Yue Pingting's mouth, it was such a relief.

Because Yue Pingting didn't want to let Xu Heng down!

In her opinion, Xu Heng taught herself so hard, she didn't get full marks in the exam, she was sorry for Xu Heng.

Because Yue Pingting was sure about all the questions except this last question, she only discussed the last question with Xu Heng.

The math roll, just turn it over like this.

But today I also took the language test.

"Xu Heng, let me ask you about Chinese, Chinese composition."

"The theme is like this..."

Yue Pingting read it to Xu Heng, "Respond with the same voice and seek the same spirit. People always pay attention to the people and things they like, and over time, they will be surrounded and shaped by similar information. In the era of smart Internet, this kind of surrounding The closer you are, the more palpable the shaping. Your future appearance may start from the next browsing you want, a series of sympathetic likes, an involuntary sharing, and a sudden touch.”

Xu Heng's first reaction was, "Create a better self."

Yue Pingting was ecstatic, "I'm relieved! I didn't digress, hahaha! I caught the point!"

"I think the composition I wrote this time is also very emotional."

"I absolutely hope that I can get better grades in the test."

Xu Heng, "What do you mean, there is hope to become the number one in the class?"

Yue Pingting's first reaction was, "You will always be number one, and I can only be number two!"

……

PS: Thank you [波] [Forgotten] [tail number 8113] for your support!Kneel for all support!Four.

Chapter 317

"I won't talk to you anymore! What! I'll hang up first!"

"There is an exam tomorrow!"

"Come on for me!"

"MUA! Good night, honey!"

Yue Pingting hung up the phone happily.

Looking up, Zhou Luzhe, Geng Xiaoyan and Zhou Xiaoya were looking at Xu Heng in front of the study door.

Xu Heng, "!!!"

"You startled me!"

Zhou Luzhe, "Girlfriend?"

"You brought your girlfriend's grade from the bottom No.1 to the top three in the class?!"

Xu Heng, "Eh...Xiaoya, you have a big mouth, what did you say to uncle?"

Zhou Xiaoya shrank her neck immediately, "Who told my sister-in-law to call you! It's so late..."

"Then my parents and my aunt asked for confirmation."

Xu Heng, "Uh..."

Zhou Luzhe, "Xu Heng, Xiaoya will be handed over to you by next week!"

Xu Heng, "%￥#@￥￥......"

Can he refuse?

Can't say no.

"Hey……"

Sighing, Xu Heng has taught Zhou Xiaoya well these few days here.

When Xu Heng left, Zhou Xiaoya felt that she had been reborn.

"Brother! Goodbye! Come here often in the future! I'll introduce my girlfriend to you..."

Xu Heng stared.

"Uh... No! I have a sister-in-law! Er... Next time you come with my sister-in-law, let me know my sister-in-law!"

Xu Heng, "%￥#@￥#%..."

After Zhou Luzhe was instructed by Xu Heng, it was like a phoenix reborn!

She was no longer restless, nor scratching her head.

Full of confidence, "I feel, I can still write 10 test papers!"

Xu Heng got into the car, and Zhou Luzhe sent him to school.

yesterday.

The monthly exams are all over.

From today to tomorrow, the class will study by itself for two days.

Xu Heng went back to school leisurely today.

Zhou Luzhe's house is not very far from Yunshan High School, just over ten minutes' drive away.

Zhou Luzhe, "Xu Heng, I'll give you a house key! This is what my aunt means. When you're free, come and play at home!"

"If you want to eat something! Tell your aunt in advance and ask her to make it for you."

Xu Heng refused, "No! Uncle! I don't want this key!"

He can't use it at all.

He is so old now, it is rare to go to Zhou Luzhe's house.

Although Zhou Luzhe and Geng Xiaoyan regarded him as their child, he was not after all, and Xu Heng still had some sense of propriety.

Come to the school gate.

Zhou Luzhe stopped immediately.

Xu Heng, "???"

Zhou Luzhe, "Just wait for me! Soon! Soon!"

He took a cigarette and ran to the doorman, "Master doorman! The child has a lot of luggage. Do me a favor. I'll send him to the door of the dormitory. I'll leave after putting down the things!"

The guard, "No, no, no! This is not allowed! You can't enter! This is the company's school policy!"

"The school is still in session now! Without permission, foreign vehicles are not allowed to enter!"

"No! No! Absolutely not!"

Zhou Luzhe, "Help me! I'll be fast! Soon! Come here, smoke a cigarette! Come to Huazi!"

Zhou Luzhe played the sophistication of the world very well.

Youdao is short-handed, and the guard is no different.

"Hurry up! Hurry up!"

"I can only drive a little bit, just enough for your car to pass by! Hurry up and come back!"

Zhou Luzhe, "Okay! Thank you!"

As soon as he turned around, Zhou Luzhe got into the car, and he was still arrogant towards Xu Heng, "How about it, does your uncle have face? If you say it, you will get in!"

"Didn't you get this kind of treatment before?"

Xu Heng, "%￥#@￥%..."

I'm afraid this uncle is not a fool!

As the car approached slowly, Zhou Luzhe rolled down the window and the doorman was polite.

The guard also looked over with a smile.

The next second!

Geek!

"Student Xu Heng?!"

moment!

The Huazi in the guard's hand is no longer fragrant!

Not only is the door wide open!

The guard even ran over!