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1、湖南长郡卫星远程学校2012年上学期制作 12反证法与放缩法+选修4-5-考一本-第二讲习题讲解Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 1
2、2不等式证明常用方法:Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12不等式证明常用方法:(1)比较法Evaluation only.Eval
3、uation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12不等式证明常用方法:(1)比较法作差法作商法Evaluation only.Evaluation only. Created with
4、 Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12不等式证明常用方法:(2)综合法(“由因导果”)(1)比较法作差法作商法Evaluation only.Evaluation only. Created with Aspose.Sli
5、des for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12不等式证明常用方法:(2)综合法(“由因导果”)(3)分析法(“执果索因”)(1)比较法作差法作商法Evaluation only.Evaluation only. Created with Aspose.
6、Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12不等式证明常用方法:(2)综合法(“由因导果”)(3)分析法(“执果索因”)(4)反证法(“正难则反”)(1)比较法作差法作商法Evaluation only.Evaluation only. Cre
7、ated with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12不等式证明常用方法:(2)综合法(“由因导果”)(3)分析法(“执果索因”)(4)反证法(“正难则反”)(5)放缩法(“整体或部分放大或缩小”)(1)比较法作差法作商
8、法Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12(6)数学归纳法( )不等式证明常用方法:(2)综合法(“由因导果”)(3)分析法(“执果索
9、因”)(4)反证法(“正难则反”)(5)放缩法(“整体或部分放大或缩小”)(1)比较法作差法作商法Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作
10、12例1.已知x, y0, 且x+y2, 试证：中至少有一个小于2。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12例2.已知a, b, c为
11、实数, a+b+c0,ab+bc+ca0, abc0, 求证：a0, b0, c0.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12例3.已知
12、a、b、c、dR+, 求证:Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12例4. 已知a、b是实数, 求证： Evaluation only
13、.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12训练1：若a、b、c都是小于1的正数, 求证：(1-a)b, (1-b)c, (1-c)a不可能同时大于Evaluation
14、 only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12训练2: 用放缩法证明：Evaluation only.Evaluation only. Created with
15、 Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12拓展1：设f(x)=x2+px+q, 求证： |f(1)|, |f(2)|, |f(3)|中至少有一个不小于Evaluation only.Evaluation only. Creat
16、ed with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程学校2012年上学期制作 12拓展2: 用放缩法证明：Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.湖南长郡卫星远程
