In binary function, why is there continuous partial derivative and the function is differentiable at a certain point, but the existence of partial derivative is only a necessary condition for differentiability?

This problem has been bothering me for a long time. Now I will talk about my understanding. In a unary function, if it is derivable at a certain point, then its critical field at this point must be continuous. According to the differentiable geometric meaning, only this point has a critical field can be differentiable

The relationship between differentiability and differentiability of binary function?

There is no difference between the two, equivalent! That is to say, differentiable must be differentiable, differentiable must also be differentiable

3x ^ 2-5x + 4 ＞ 0,

3x²－5x＋4＞0
3(x²－5/3x)＋4＞0
3(x - 5/6)²+13/12＞0
∵(x - 5/6)²≥0
The establishment of shangshiheng
X takes any real number

A rectangular vegetable field, 110 meters long and 44 meters wide. Draw it on a 1:2000 scale plan. How many centimeters should it be long and wide?

The length is 110 × 100 △ 2000 = 5.5cm
The width is 44 × 100 △ 2000 = 2.2 cm

The composition about dream
To junior high school!

Dream, is necessary for every successful person; dream, is great, we need to practice to pursue. On the first day of school, the teacher told us to watch the TV program - "the first lesson of school" gave me great inspiration
There are so many people in it that I admire them. Among them, the two elder brothers Yang mengheng and Liu Wei are the most admired. Although they are disabled, they have no hands. However, they have not given up their dreams, worked hard, practiced their dreams, achieved success, and achieved things that even ordinary people can't do
Einstein once said: "success lies in 99% of sweat and 1% of effort." I think this sentence is very reasonable. The above two big brothers have good results because they persevere, do not give up, and strive to pursue their dreams. This is the magic and great power of dreams. Everyone should have their own dreams and strive towards them
My dream is to be an excellent entrepreneur, to serve the country until death, to help the children in trouble, to let their hearts have the sunshine, to work hard to complete their dreams. Don't think this is impossible, because if we fight in the direction of dreams, everything is possible. My wish is to help all the children to complete their dreams, maybe I can't, But one day my descendants will be able to. The disabled children should not feel inferior, but should face life bravely. They should know that there will be hope if they have dreams, and that living is the best thing. Just like brother Liu Wei said, "I have two ways to go now, either to die quickly or to live brilliantly." if my dream comes true, I will do as I say, wait for my good news!
My dream, Chinese dream; Chinese dream is my dream. Students, cheer for your dream! Hope is a dream, and dream is hope. But dreams need to be pursued and practiced. Cheer for your dreams!
let your dreams fly
A candidate in Henan
If your faith is still standing, no one can make you fall
——Martin Luther King
After a winter's silence, butterfly has accumulated all her strength and finally turned the dream of flying into reality. After five years of silence, yimifua broke out all her life's hard work and finally revealed the fragrance of flowers to everyone. Firm your faith and let go of your dream, and you will dominate your world
"Heaven will bring down great responsibility, so people must first work hard, work hard, starve their body and skin, lack their body..." Sun Bin endured the torture of removing his knee bone. He persevered and persevered in completing the art of war of Sun Bin, a military book that has been handed down for thousands of years. Sun Bin, how many people are impressed by your learning, and how many people are attracted by your wisdom. In silence, you rely on your firm belief to fly your dream into the blue sky. Let your dream fly, don't forget your firm belief!
"Heaven is healthy, and a gentleman is constantly striving for self-improvement." this sentence has inspired many people with lofty ideals, and has given many people who have lost their way a new life. A Bing, the blind composer, you feel deeply shocked in the wandering of "a few happy families and a few sad families", so a song "Er Quan Ying Yue" is born in your erhu, Everyone was moved. When Xiao zele finished his command, he knelt down excitedly. "This song should only be heard in the sky. How many times can the world smell it?" although your eyes are blind, there is a lamp of faith in your heart for you to navigate. Under the guidance of the heart lamp, you fly your dream to the music hall and create a new world of national music.
How can you forget Zhuge Liang's figure in Nanshan? Your talent makes Liu Bei look at the cottage without regret, your natural and unrestrained makes the Confucians unable to argue, and you are able to do it well. This is the crystallization of your diligence. "The fragrance of wine is not afraid of the deep alley", "the peach and the plum are silent, and the next one is strange". You know that your painstaking efforts will be rewarded eventually. You are just waiting for your dream to come true, You are natural and unrestrained; seven capture Meng Huo, you are calm and calm. Under the support of faith, you have created the great cause of heaven and earth
Set up faith, fly dream, you will be able to reach a beautiful place with it. Set up faith, fly dream, you will have a more brilliant tomorrow. Let dream fly, let faith bloom
Dream dancing in reality
Looking up at the starry sky, it seems that there are no flawed stars shining in the Milky way, which gives us unlimited reverie. In the starry sky free of dust, many people have beautiful dreams. The people who fly to the stars know that there are dust and debris, just like the earth, so they lose the freedom and right of fantasy. We can't just indulge in our own fantasy, But we can't let the free flying thoughts be buried in the merciless reality
Ruan Ji witnessed the world's muddle and the different places of his friends, and escaped from reality through drunkenness. He had been escaping, escaping and escaping all his life, but he was finally rejected because of a piece of "Wei Zheng Chong vs. Jin Wang Jian". Ji Kang was totally living in reality and refused to make any agreement with life, In fact, one step forward from Ruan Ji's drunkenness is Ji Kang's Guangling San, and one step backward from Ji Kang's Guangling San is Ruan Ji's drunkenness. The circumstances of the same fate are so different. If two people take a step in the middle and make a little balance between fantasy and reality, maybe they won't lead the living into illusion, How can we let those who look up to the stars understand the reality, and how can those who fly to the stars keep their dreams? In that era when everyone complained, Shen Congwen witnessed the cruelty of reality, but still wrote that small town in the south of the Yangtze River as a paradise with beautiful mountains, beautiful water and beautiful people, He looked at the society and his life with the most primitive emotion and a childlike heart. He did not indulge in his fantasy, nor let reality numb his mind
Mr. Zhang Yunhe is also a wise old man. He has experienced great wealth, wars and ten years of catastrophe in his life. However, he always has a feeling of compassion and a childlike innocence. His compassion makes him face up to the reality and overcome it, And his childlike innocence makes him never give up his fantasy and power in any difficult situation
Kawabata Yasunari's simple sentence "at four o'clock in the morning, I see the crabapple flower sleepless" touched many hearts in a moment. This is the perfect combination of dream and reality, which makes those worldly things collapse in an instant, and warms many hearts that are increasingly numb in reality
Face reality but not commit to it; keep fantasy but not indulge in it. Let dream dance in reality
Full mark composition of college entrance examination: Wings of dream
The snail slowly crawls towards the top of the pyramid, even in the hot sun, because the snail believes that although I don't have the strength of an eagle, perseverance is my greatest talent; the spider has no wings, but it can knot the web in the air, because the spider believes that dream is the best wing; the leaf still sticks to the branch in the wind and rain, Because the leaves believe that a lifetime of persistent green will come in exchange for a golden autumn And I believe that if you put wings on your dream, you can soar to the sky
Maybe the flowers on the roadside will laugh at me. Why are you so tired? You are just in vain. Maybe the birds in the sky will laugh at me. Flying should be gifted. Maybe the clouds in the sky will laugh at me. I (you) and I are far away from each other. However, I will tell them with a smile that there are too many frustrations, but I believe that heaven rewards diligence
Isn't that child, who was considered by the teacher to be low IQ and expelled from school, also become the "king of invention" through his unremitting efforts? Isn't that person who repeatedly went to the editorial department to reject manuscripts and was so poor that he had to be accompanied by a mouse, and finally became a world-renowned animation founder? That girl who was eager to become a model but was rejected by the model company, I believe that if I have a dream, I will have hope
Yao Ming told us: "the opportunity is fleeting. If you work hard, you may not succeed, but if you give up, you will fail." Tai Lihua told us that everyone is in their own hands, and no one can beat us
Who would have thought that the distance of 100 meters will no longer be the distance between China and the world, and the railings will no longer be the obstacle for the Chinese people to move forward, but Liu Xiang said, I'm here to win the championship. Liu Xiang's self-confidence has created the possibility for his dream. His hard work has made China's national flag fly high over the world
There is no moment for Chinese people to look up at the sky for such a long time. In the dark blue sky, we are looking for two pairs of eyes. 115 hours of space roaming has achieved many dreams of flying in the sky that the Chinese people yearn for. At that moment, we can say with pride that the flying in Dunhuang murals has become a reality, which is the result of our efforts
When I stand at the door of my home, the snail tells me to carry my luggage and start out, and the dream is the best reason; the spider tells me that if there is no dream, even the wings will become a burden; the leaf tells me never to lament, green all your life, and then mature into a golden dream. I tell myself that if you have a dream, you have to pursue it
Vibration dream wings, take off!

Known: three consecutive odd numbers, their sum of squares is 251, find these three odd numbers

Let these three odd numbers be n-2, N, N + 2 in turn, where n is a natural number, then n > 2, then according to the problem meaning, we can get the following equation: (n-2) 2 + N2 + (n + 2) 2 = 251, 3N2 = 243, N2 = 81, n = 9 or n = - 9, when n = 9, n-2 = 7, N + 2 = 11; when n = - 9, n-2 = - 11, N + 2 = - 7; answer: these three consecutive odd numbers are 7, 9, 11 or - 7, - 9, - 11

Cutting bottom and height are 0.2 meters right triangle. A 21 meters long, 16 meters wide rectangle, can cut such a triangle up to a few?

Combine two triangle hypotenuse together to form a square with side length of 0.2m, that is to say, a square with side length of 0.2m can be cut into two triangles as you require. Next, consider whether the rectangle can be completely cut into a square with side length of 0.2m without surplus: 21 △ 0.2 = 105,16

In binary function, why is there continuous partial derivative and the function is differentiable at a certain point, but the existence of partial derivative is only a necessary condition for differentiability?