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1、课题：含有绝对值的不等式课题：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. 绝对值的概念绝对值的概念|a|=( a0 ),( a =0 ),(a 0,则则 |x|a -axa-aao（）若，则（）若，则或或a-aoEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2
2、004-2011 Aspose Pty Ltd. 定理引入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 Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.定理证明定理证明证法二证法二先证先证:Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspos
3、e Pty Ltd.下面证明下面证明: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|变形变形:结合定理和变形又可变式为结合定理和变形又可变式为|a|-|b|a+b|a|+|b|Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5
4、.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.若若|a-c|h , |b-c| h ,则下列不等式一定成立的是（则下列不等式一定成立的是
5、（ ）(A) |a-b|h (C) |a-b|h2. 已知已知 |a-c|1 , 求证求证 |a| |c|+1A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 Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-201
6、1 Aspose Pty Ltd.例例2 已知函数已知函数y=|x|-|x-3| ,求函数的求函数的值值域域解法1 : 利用函数法-3330xy通过图像观察函数的值域为-3，3Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.解法2 利用不等式法由由 | |x|-|x-3| | x-(x-3) |=3得：得：-3|x|-|x-3|3-3y3, 即即y-3,3Evaluation only.Created with As
7、pose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.2.函数y=|x|-|x+3|的值域是3.函数y=|x-2|-|x-3|的值域是-3，3-1，1Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.小结本节课我们主要学习了以下主要内容本节课我们主要学习了以下主要内容1.绝对值不等式基本定理以及其绝对值不等式
8、基本定理以及其2个推论个推论.2.绝对值不等式基本定理的主要应用，特绝对值不等式基本定理的主要应用，特别是在解决某些函数值域时更显优越性别是在解决某些函数值域时更显优越性.知识的建构绝对值不 等式定理绝对值不等式定理的两个重要的推论应用(证明不等式,求值域Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd. 作业课本课本22页习题页习题 6.5 第第1，2，3 题题. Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.
