《极限的运算和两个重要极限.ppt

求极限方法举例 小结 二、两个重要极限 小结 三、无穷小的比较 等价无穷小代换 小结 例３ 解 若未定式的分子或分母为若干个因子的乘积，则可对其中的任意一个或几个无穷小因子作等价无穷小代换，而不会改变原式的极限． Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 不能滥用等价无穷小代换. 切记，只可对函数的因子作等价无穷小代换，对于代数和中各无穷小不能分别代换. 注意 例４ 解 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例５ 解 解 错 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例6 解 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. * §2、3 极限的运算和两个重要极限 一、极限的四则运算 二、两个重要极限 三、无穷小量的比较 说明：记号“lim”下面没有标明自变量的变化过程，实际上，下面的定理对x→X0及x→∞都成立。我们只证明x→X0的情形。 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 由无穷小运算法则,得 一、极限的四则运算 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 推论1 常数因子可以提到极限记号外面. 推论2 有界， Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例1 解 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 小结: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解 商的法则不能用 由无穷小与无穷大的关系,得 例2 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解 例3 (消去零因子法) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例4 解 (无穷小因子分出法) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 小结: 无穷小分出法:以分母中自变量的最高次幂除分子,分母,以分出无穷小,然后再求极限. Evaluation only. Creat