Their feelings are fast, each 40 words will be handed over tomorrow, hurry up, there will be heavy t

4. First find the full differential dz of z

The coefficients in front of dx and dy are respectively.

The partial derivatives of z to x and y.

5. Chain rule.

First, find the partial derivative of z versus x.

Then find the second-order mixed partial derivative.

The process is as follows: 6) The implicit function is derived, and any point on the surface is obtained.

The normal vector of the tangent plane.

The coordinates of the substitution point.

Point French, to get the tangent plane equation.

The process is as follows: 7) Find the two first-order partial derivatives of z.

Get the possible extreme points, 4.

The second-order partial derivative is then used to determine the type of extreme point.

The maximum value of z is 0

The minimum value of z is -8

The process is as follows: 8) Set up two right-angled edges.

The Lagrange multiplier method finds conditional extremums.

The process is as follows:

4.Let f(x,y,z)=ze x-sinxz-xy fx=ze x-zcosxz-y

fy=-2xy

fz=e^x-xcosxz

z/∂x=-fx/fz

z/∂y=-fy/fz

Substituting the above equation can be obtained.

6.Let f(x,y,z)=2x +y +z-6fx=4x,fx(-1,1,3)=-4

fy=2y,fy(-1,1,3)=2

fz=1,fz(-1,1,3)=1

So the tangent plane equation is.

4(x+1)+2(y-1)+(z-3)=0, that is, 4x-2y-z+9=0

During the National Day holiday, I read a book called "Daddy's Pigeon", and I learned Xu Dao by reading this book

The philosophy of life is multi-life, and the inner part also understands the author's guilt.

Tolerance. At the beginning, it is narrated that the author's mother was absent when he was very young, and the author compares himself to a wild pigeon, flying lonely in search of his mother, longing for his mother's love. Dad gave his love to "me", but whenever he saw someone else's mother coming, "I" tears flowed, and then "I" chose to exile like a wild pigeon, childhood "I" lived with my grandmother and grandfather, when I was very young, I lived in an alley by the river in the countryside, "I" often played there, and the street market was very lively:

The shouts of the vegetable sellers and the bargaining voices of the vegetable buyers make "me" nostalgic for a long time....

This is a very good book, my feelings may not be comprehensive, the emotions and thoughts of the characters in the book have to be slowly experienced in order to understand the author's touching points. I hope more people can read this book, it can help you cultivate your sentiments, wash away your bad habits, and change yourself.

Everyone has a favorite teacher, and I am no exception, whenever I look at the ** I am with the teacher, I always think of the most memorable teacher in my heart - Mr. Huang Mingxin.

Mr. Huang is a Chinese teacher at a school in Shenzhen, about 28 years old this year, with a pair of dimples on her white and dignified face and a pair of glasses on the high bridge of her nose, which makes her more knowledgeable.

I remember one time, Ms. Huang asked me and a few classmates to go to her office to correct homework. As soon as I entered the office, I saw Mr. Huang sitting at his desk correcting one test paper after another. We listened to the teacher's arrangement, changed the homework for a while, and listened to the math teacher say to Mr. Huang

Ah Huang, you have a cold today, and I only learned in the morning that you have a fever again, don't go back too late, go back early to rest! "Oh, thank you, I'm fine, there's still a class of homework that hasn't been changed! Before she could finish speaking, she coughed again, and the teacher said to us again

Students, it's not early, go back first, and pay attention to safety on the road. "A few of our classmates went home, and it wasn't until the next morning that I found out that Mr. Huang had come home late last night.

Ms. Huang is not only conscientious about the little things at work, but she is also very understanding, and treats us like her own children, not long after I came to this class, the teacher found that my Mandarin is good, reading the text aloud is very emotional, and I heard the teachers of each subject say that I am self-motivated. Teacher Huang called me to the office, who was a little introverted, and said to me kindly: "Chen Yufei, you are a new student, your performance during this period of time is seen by the teacher, the teacher knows that you are an excellent student, can you read a text to the teacher?"

I nodded, forgetting the restraints, the nervousness I had at the beginning, and the teacher standing in front of me, as if it was my friend, and I read aloud with a fluttering eyebrow. After reading aloud, Mr. Huang said to me, "You read with emotion, and the teacher thinks you are very suitable to be our school host, but let's start from a young age, shall we?"

The teacher saw that you were a good seedling, and the school asked our class to select a school announcer, well, the teacher chose you. When I heard this, my face was filled with excitement. When I was a little nervous at the beginning of the broadcast, Ms. Huang would encourage me, and her kind face and gentle tone made me feel loved.

After the guidance and encouragement of my teacher, I became more and more relaxed in the broadcast studio.

Over the past few years, Mr. Huang has worked hard to educate us, silently encouraging and supporting us behind the scenes. Perhaps, Ms. Huang has forgotten how many times she has been busy with the illness of her students, and has forgotten the hardships she has paid. However, as a student, I will never forget and clearly understand that everything she gave was for her students.

The teacher-student relationship in the past six years is like a record forever.

Ten years of trees, 100 years of people; The grace of the willow is unforgettable.

After graduating from junior high school, Hua Luogeng became an assistant in the Department of Mathematics of Tsinghua University. The following year, his ** began to be published in famous foreign mathematics journals. Tsinghua University broke a precedent and decided to promote Hua Luogeng, who only had a junior high school education, to a teaching assistant.

In the 16th century, the German mathematician Rudolph spent his whole life calculating pi to 35 decimal places, which later generations called Rudolph's number, and after his death, others engraved this number on his tombstone.