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Chapter 28

Chapter 28. INEQUALITIES. 不等式. What will be taught in this chapter?. 1. Some fundamental properties of inequalities. 2. Logarithmic function inequalities. 3 . absolute function inequalities. Use the To determine relationship between coeff. and roots. Some properties of inequalities.

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Chapter 28

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  1. Chapter 28 INEQUALITIES 不等式 FYHS-Kulai by Chtan

  2. What will be taught in this chapter? 1. Some fundamental properties of inequalities. 2. Logarithmic function inequalities. 3. absolute function inequalities. Use the To determine relationship between coeff. and roots. FYHS-Kulai by Chtan

  3. Some properties of inequalities FYHS-Kulai by Chtan

  4. 2 3 4 5 FYHS-Kulai by Chtan

  5. 6 7 9. FYHS-Kulai by Chtan

  6. 10. 11. 12. FYHS-Kulai by Chtan

  7. 13. have same sign. have opposite sign. FYHS-Kulai by Chtan

  8. Some common inequalities formulae FYHS-Kulai by Chtan

  9. Equality holds when 2 Equality holds when FYHS-Kulai by Chtan

  10. 3 Equality holds when 4 Equality holds when AM-GM inequality FYHS-Kulai by Chtan

  11. 5 Equality holds when 6 Equality holds when FYHS-Kulai by Chtan

  12. 7 Equality holds when Equality holds when FYHS- Kulai by Chtan

  13. e.g.1 Consider the function FYHS-Kulai by Chtan

  14. Soln : FYHS-Kulai by Chtan

  15. FYHS-Kulai by Chtan

  16. 9 10 1 FYHS-Kulai by Chtan

  17. 13 14 FYHS-Kulai by Chtan

  18. FYHS-Kulai by Chtan

  19. Exponential inequalities To solve this inequality, it is equivalent to solve : FYHS-Kulai by Chtan

  20. To solve this inequality, it is equivalent to solve : FYHS-Kulai by Chtan

  21. logarithmic inequalities It is equivalent to solve : FYHS-Kulai by Chtan

  22. It is equivalent to solve : FYHS-Kulai by Chtan

  23. e.g.2 FYHS-Kulai by Chtan

  24. e.g.3 : FYHS-Kulai by Chtan

  25. e.g.4 Find the range of values of x for which : FYHS-Kulai by Chtan

  26. e.g.5 Find the range of values of x for which : FYHS-Kulai by Chtan

  27. e.g.6 : FYHS-Kulai by Chtan

  28. e.g.7 Express in the modulus form : FYHS-Kulai by Chtan

  29. e.g.8 Express in the modulus form : FYHS-Kulai by Chtan

  30. e.g.9 For what values of x is : FYHS-Kulai by Chtan

  31. e.g.10 : FYHS-Kulai by Chtan

  32. e.g.11 : FYHS-Kulai by Chtan

  33. e.g.12 : FYHS-Kulai by Chtan

  34. e.g.13 : FYHS-Kulai by Chtan

  35. e.g.14 FYHS-Kulai by Chtan

  36. e.g.15 . FYHS-Kulai by Chtan

  37. e.g.16 For what values of x is : positive . FYHS-Kulai by Chtan

  38. e.g.17 Find the range of values of x which satisfy the inequality : FYHS-Kulai by Chtan

  39. e.g.18 Find the range of values of x which satisfy the inequality : FYHS-Kulai by Chtan

  40. e.g.19 For what values of x is : FYHS-Kulai by Chtan

  41. e.g.20 Solve the inequality : FYHS-Kulai by Chtan

  42. e.g.21 For what values of x is : FYHS-Kulai by Chtan

  43. Harder examples FYHS-Kulai by Chtan

  44. e.g.22 FYHS-Kulai by Chtan

  45. Soln : Using AM-GM inequality, consider the 3 numbers : FYHS-Kulai by Chtan

  46. Similarly, and Adding the 3 inequalities, FYHS-Kulai by Chtan

  47. FYHS-Kulai by Chtan

  48. e.g.23 FYHS-Kulai by Chtan

  49. Soln : (i) Given Using AM-GM inequality, consider the 4 numbers : : FYHS-Kulai by Chtan

  50. FYHS-Kulai by Chtan

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