Chapter 28 INEQUALITIES FYHSKulai by Chtan 1 What
Chapter 28 INEQUALITIES 不等式 FYHS-Kulai by Chtan 1
What will be taught in this chapter? 1. Some fundamental properties of inequalities. 2. Logarithmic function inequalities. 3. absolute function inequalities. FYHS-Kulai by Chtan 2
Some properties of inequalities FYHS-Kulai by Chtan 3
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have same sign. have opposite sign. FYHS-Kulai by Chtan 7
Proof : (8) FYHS-Kulai by Chtan 8
Proof : (9) FYHS-Kulai by Chtan 9
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Proof : (10) FYHS-Kulai by Chtan 11
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Some common inequalities formulae FYHS-Kulai by Chtan 16
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AM-GM inequality FYHS-Kulai by Chtan 18
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e. g. 1 Consider the function FYHS-Kulai by Chtan 21
Soln : FYHS-Kulai by Chtan 22
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Exponential inequalities To solve this inequality, it is equivalent to solve : FYHS-Kulai by Chtan 27
To solve this inequality, it is equivalent to solve : FYHS-Kulai by Chtan 28
logarithmic inequalities It is equivalent to solve : FYHS-Kulai by Chtan 29
It is equivalent to solve : FYHS-Kulai by Chtan 30
e. g. 2 FYHS-Kulai by Chtan 31
e. g. 3 FYHS-Kulai by Chtan 32
e. g. 4 Find the range of values of x for which : FYHS-Kulai by Chtan 33
e. g. 5 Find the range of values of x for which : FYHS-Kulai by Chtan 34
e. g. 6 FYHS-Kulai by Chtan 35
e. g. 7 Express in the modulus form : FYHS-Kulai by Chtan 36
e. g. 8 Express in the modulus form : FYHS-Kulai by Chtan 37
e. g. 9 For what values of x is : FYHS-Kulai by Chtan 38
e. g. 10 FYHS-Kulai by Chtan 39
e. g. 11 FYHS-Kulai by Chtan 40
e. g. 12 FYHS-Kulai by Chtan 41
e. g. 13 FYHS-Kulai by Chtan 42
e. g. 14 FYHS-Kulai by Chtan 43
e. g. 15 FYHS-Kulai by Chtan 44
e. g. 16 For what values of x is : positive. FYHS-Kulai by Chtan 45
e. g. 17 Find the range of values of x which satisfy the inequality : FYHS-Kulai by Chtan 46
e. g. 18 Find the range of values of x which satisfy the inequality : FYHS-Kulai by Chtan 47
e. g. 19 For what values of x is : FYHS-Kulai by Chtan 48
e. g. 20 Solve the inequality : FYHS-Kulai by Chtan 49
e. g. 21 For what values of x is : FYHS-Kulai by Chtan 50
Harder examples FYHS-Kulai by Chtan 51
e. g. 22 FYHS-Kulai by Chtan 52
Soln : FYHS-Kulai by Chtan 53
Similarly, and Adding the 3 inequalities, FYHS-Kulai by Chtan 54
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e. g. 23 FYHS-Kulai by Chtan 56
Soln : (i) Given FYHS-Kulai by Chtan 57
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(ii) FYHS-Kulai by Chtan 60
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FYHS-Kulai by Chtan 2+9+0 -27 -3 -6 -9 27 2 3 -9 0 -3 -6 +9 63 2 -3 0
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Q: FYHS-Kulai by Chtan 65
The notorious cases : FYHS-Kulai by Chtan 66
When will you use this ? FYHS-Kulai by Chtan 67
1. Find the maximum and minimum values of : FYHS-Kulai by Chtan 68
2. Find the range of the function : FYHS-Kulai by Chtan 69
so that the equation has equal roots, no real roots or 2 real roots. FYHS-Kulai by Chtan 70
can take all real values. FYHS-Kulai by Chtan 71
5. Many other cases … Let me tell when I got the ideas… FYHS-Kulai by Chtan 72
Addendum 附录 FYHS-Kulai by Chtan 73
1. reduction to absurdity -- proof by contradiction 反证法 FYHS-Kulai by Chtan 74
e. g. FYHS-Kulai by Chtan 75
Soln : FYHS-Kulai by Chtan 76
Proved. FYHS-Kulai by Chtan 77
2. Solve the inequalities : FYHS-Kulai by Chtan 78
3. Solve the inequalities : FYHS-Kulai by Chtan 79
4. Solve the inequalities : FYHS-Kulai by Chtan 80
5. Solve the inequalities : FYHS-Kulai by Chtan 81
6. Solve the irrational inequalities : FYHS-Kulai by Chtan 82
The end FYHS-Kulai by Chtan 83
- Slides: 83
