Western Normal University Edition First Grade Mathematics Volume 1
Beijing Normal University Edition Seventh Grade Mathematics Volume 1
People's Education Press First Grade Mathematics Volume 1
People's Education Press Second Grade Mathematics Volume 1
People's Education Press Third Grade Mathematics Volume 1
Hebei Education Edition Third Grade Mathematics Volume 1
Beijing Normal University Edition Seventh Grade Mathematics Volume 2
Beijing Normal University Edition Fifth Grade Mathematics Volume 1
Qingdao Edition Seventh Grade Mathematics Volume 1
Beijing Normal University Edition Eighth Grade Mathematics Volume 1
Hebei Education Edition Seventh Grade Mathematics Volume 2
People's Education High School Mathematics Edition B Compulsory Course 2
Jiangsu Education Edition Fourth Grade Mathematics Volume 1
People's Education Press First Grade Mathematics Volume 2
Qingdao Edition Seventh Grade Mathematics Volume 2
Beijing Normal University Edition Fifth Grade Mathematics Volume 2
Category | Format | Size |
---|---|---|
People's Education High School Mathematics Edition A Compulsory Course 1 | pptx | 6 MB |
Description
"Basic Inequalities" Quadratic Functions, Equations and Inequalities PPT Courseware (First Lesson Basic Inequalities)
Part One: Learning Objectives
1. Understand the proof process of basic inequalities. (emphasis)
2. Be able to use basic inequalities to prove simple inequalities and compare the sizes of algebraic expressions.
core competencies
1. Cultivate logical reasoning skills through the proof of inequalities.
2. Use basic inequality forms to solve simple optimal value problems and improve your mathematical operation literacy.
Basic Inequalities PPT, Part 2: Independent preview to explore new knowledge
A preliminary exploration of new knowledge
1. important inequalities
∀a, b∈R, there is a2+b2≥_______, if and only if _______, the equal sign is true.
2. basic inequalities
(1) Related concepts: When a and b are both positive numbers, a + b2 is called the arithmetic mean of the positive numbers a and b, and ab is called the geometric mean of the positive numbers a and b.
(2) Inequality: When a and b are any positive real numbers, the geometric mean of a and b is not greater than their arithmetic mean, that is, ab≤a+b2. The equal sign holds true if and only if _______.
First try
1. The condition for the establishment of the equal sign of the inequality a2+1≥2a is ()
A. a=±1
B. a=1
C. a=-1
D. a=0
2. It is known that a, b∈(0,1), and a≠b, the largest of the following formulas is ()
A. a2+b2
B. 2ab
C. 2ab
D. a+b
3. It is known that ab=1, a>0, b>0, then the minimum value of a+b is ()
A. 1B. 2
C. 4D. 8
Basic Inequalities PPT, Part 3: Collaborative exploration to improve literacy
Understanding basic inequalities
[Example 1] The following four derivation processes are given:
①∵a and b are positive real numbers, ∴ba+ab≥2ba·ab=2;
②∵a∈R, a≠0, ∴4a+a≥24a·a=4;
③∵x, y∈R, xy<0, ∴xy+yx=--xy+-yx≤-2-xy-yx=-2.
The correct derivation is ()
A. ①②B. ①③
C. ②③ D. ①②③
B ①∵a and b are positive real numbers, ∴ba and ab are positive real numbers, which meet the conditions of basic inequalities, so the derivation of ① is correct.
②∵a∈R, a≠0, does not meet the conditions of basic inequality,
∴4a+a≥24a·a=4 is wrong.
③ From xy < 0, we get that xy and yx are both negative numbers. However, after the negative sign of the overall xy + yx is raised during the derivation process, -xy and -yx both become positive numbers, which meets the conditions of mean inequality, so ③ is correct. ]
regular method
1. The basic inequality ab≤a+b2 (a>0, b>0) reflects the relationship between the sum and product of two positive numbers.
2. To accurately grasp basic inequalities, we must grasp the following two aspects: (1) The condition for the establishment of the theorem is that a and b are both positive numbers. (2) The meaning of "if and only if": when a=b, the equality of ab≤a+b2 holds true, that is, a=b⇒a+b2=ab; only when a=b, the equality of a+b2≥ab holds, That is, a+b2=ab⇒a=b.
Basic Inequalities PPT, Part 4: Complying with Standards and Solidifying Basics in Class
1. Thinking and analysis
(1) For any a, b∈R, a2+b2≥2ab, a+b≥2ab are all true. ()
(2) If a≠0, then a+1a≥2a·1a=2.()
(3) If a>0, b>0, then ab≤a+b22.()
[Tips] (1) For any a, b∈R, a2+b2≥2ab holds. When a and b are both positive numbers, the inequality a+b≥2ab holds.
(2) Only when a>0, according to the basic inequality, the inequality a+1a≥2a·1a=2 holds.
(3) Because ab≤a+b2, so ab≤a+b22.
2. Assuming a>b>0, then the following inequalities must be true ()
A. a-b<0
File Info
Update Time: 2024-10-01
This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template
"Basic Inequalities" Quadratic Functions, Equations and Inequalities PPT Courseware (First Lesson Basic Inequalities) Simple campus recruitment activity planning plan summary enterprise and institution recruitment publicity lecture PPT template is a general PPT template for business post competition provided by the manuscript PPT, simple campus recruitment activity planning plan summary enterprise and institution recruitment promotion Lecture PPT template, you can edit and modify the text and pictures in the source file by downloading the source file. If you want more exquisite business PPT templates, you can come to grid resource. Doug resource PPT, massive PPT template slide material download, we only make high-quality PPT templates!
Tips: If you open the template and feel that it is not suitable for all your needs, you can search for related content "Basic Inequalities" Quadratic Functions, Equations and Inequalities PPT Courseware (First Lesson Basic Inequalities) is enough.
How to use the Windows system template
Directly decompress the file and use it with office or wps
How to use the Mac system template
Directly decompress the file and use it Office or wps can be used
Related reading
For more detailed PPT-related tutorials and font tutorials, you can view: Click to see
How to create a high-quality technological sense PPT? 4 ways to share the bottom of the box
Notice
Do not download in WeChat, Zhihu, QQ, built-in browsers, please use mobile browsers to download! If you are a mobile phone user, please download it on your computer!
1. The manuscript PPT is only for study and reference, please delete it 24 hours after downloading.
2. If the resource involves your legitimate rights and interests, delete it immediately.
3. Contact information: service@daogebangong.com
"Basic Inequalities" Quadratic Functions, Equations and Inequalities PPT Courseware (First Lesson Basic Inequalities), due to usage restrictions, it is only for personal study and reference use. For commercial use, please go to the relevant official website for authorization.
(Personal non-commercial use refers to the use of this font to complete the display of personal works, including but not limited to the design of personal papers, resumes, etc.)