[高一数学必修绝对值不等式ppt.ppt

* * 课题：含有绝对值的不等式 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1. 绝对值的概念 |a|= ( a0 ), ( a =0 ), (a 0 ) . ｛ a 0 -a 2. |a|的几何意义： 数轴上表示实数a的点与原点 间的距离. 基础知识回顾 3. 绝对值的基本运算性质 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 4. 含绝对值不等式的解法 (１) 若a 0,则 |x|﹤a -axa -a a o （２）若ａ＞０，则｜ｘ｜＞ａ Ｘ＞ａ或ｘ＜－ａ a -a o Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 定理引入 试考虑两数和的绝对值与两数绝对值的和与差的关系，请填表观察． ０ １ １ ２ －１ －２ ２ －３ －３ １ １ ３ ３ ５ ４ １ ３ ３ １ ２ －１ －１ －１ －１ ２ ａ ｂ ｜ａ｜＋｜ｂ｜ ｜ａ＋ｂ｜ ｜ａ｜－｜ｂ｜ ｜ａ｜－｜ｂ｜≤｜ａ＋ｂ｜≤｜ａ｜＋｜ｂ｜ Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 定理证明 证法二 先证:｜ａ＋ｂ｜≤｜ａ｜＋｜ｂ｜ Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 下面证明:｜ａ｜－｜ｂ｜≤｜ａ＋ｂ｜ Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 定理变式 变形: 把定理中的a换为b,b换为a,定理可变式为 |b|-|a|≤|a+b| ≤|a|+|b| 变形:结合定理和变形又可变式为 ︱|a|-|b|︱≤|a+b|≤|a|+|b| ｜ａ｜－｜ｂ｜≤｜ａ＋ｂ｜≤｜ａ｜＋｜ｂ｜ Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 把定理中的b换为-b可变形为 |a|-|-b|≤|a-b| ≤|a|+|-b| （5）|a+b|-|a-b| 2|a| |a+b|+|a-b| ≤ ≤ |a+b|-|a-b| 2|b| |a+b|+|a-b| ≤ ≤ 试一试 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1.若|a-c|h , |b-c| h ,则下列不等式一定成立的是（ ） (A) |a-b|2h (B) |a-b|h (C) |a-b|h (D) |a-b|h 2. 已知 |a-c|1 , 求证 |a| |c|+1 A 提示：|a|= |a-c+c|≤|a-c|+|c|1+|c| Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 定理应用 Evaluation only. Created with