《微积分上册习题一》由会员分享，可在线阅读，更多相关《微积分上册习题一（59页珍藏版）》请在金锄头文库上搜索。
1、（一）函数的定义（二）极限的概念（三）连续的概念一、主要内容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.函 数 的定义反函数隐函数反函数与直接 函数之间关系基本初等函数复合函数初等函数
2、函 数 的性质单值与多值 奇偶性 单调性 有界性 周期性双曲函数与 反双曲函数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.1、函数的定义Evaluation only.Evaluati
3、on 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.函数的分类函数初等函数非初等函数(分段函数,有无穷多项等函数)代数函数超越函数有理函数无理函数有理整函数(多项式函数)有理分函数(分式函数)Evaluation only.Evaluati
4、on 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.(1) 单值性与多值性:2、函数的性质Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Cl
5、ient 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.(2) 函数的奇偶性:偶函数奇函数yxoEvaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides fo
6、r .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.(3) 函数的单调性:设函数f(x)的定义域为D，区间I D，如果对于区间I上 任意两点 及 ，当 时，恒有：(1) ,则称函数 在区间I上是单调增加的；或(2) , 则称函数 在区间I上是单调递减的；单调增加和单调减少的函数统称为单调函数。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 C
7、lient 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.(4) 函数的有界性: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
8、.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.设函数 f(x) 的定义域为D，如果存在一个不为零的 数l,使得对于任一 ,有 .且 f(x+l)=f(x) 恒成立,则称f(x)为周期函数,l 称为 f(x) 的周期.（通常 说周期函数的周期是指其最小正周期）.(5) 函数的周期性:oyxEvaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Pr
9、ofile 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.3、反函数4、隐函数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
10、 Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.5、反函数与直接函数之间的关系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.Co
11、pyright 2004-2011 Aspose Pty Ltd.6、基本初等函数1）幂函数2）指数函数3）对数函数4）三角函数5）反三角函数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
12、.7、复合函数8、初等函数由常数和基本初等函数经过有限次四则运算和有 限次的函数复合步骤所构成并可用一个式子表示 的函数,称为初等函数.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.9、
13、双曲函数与反双曲函数双曲函数常用公式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.Evaluation only.Evaluation only. Created with Aspose
14、.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.左右极限两个重要 极限求极限的常用方法无穷小 的性质极限存在的 充要条件判定极限 存在的准则无穷小的比较极限的性质数列极限函 数 极 限等价无穷小 及其性质唯一性无穷小两者的 关系无穷大Evaluation only.Evaluation on
15、ly. 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.1、极限的定义Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.
16、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.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.左极限右极限Eva
