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2022年教案第一章函数与极限 .pdf

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1、高等数学教案第 1、2 讲章节次数第 1、2 讲：第一章函数与极限，第一节映射与函数教学目的要求1.理解函数的概念。2.掌握函数的初等函数的性质及其图形。3.会建立简单应用问题中的函数关系式。主要内容集合、映射、函数函数的几种几何特性反函数、复合函数、初等函数常见的经济函数重点难点理解复合函数及分段函数，反函数及隐函数的概念，基本初等函数的性质及其图形。教学方法讲授，练习课后作业作业：第1 讲：21 22 页的习题4、5、6、7、10 第 2 讲：22 页的习题11、12、14、15、16 备注本章内容带有复习性质，凡中学已经学习过的有关函数的知识，只需加以复习提高，不必再作详细讲解。课程的性

2、质与任务高等数学是高等院校学生必修的一门重要基础理论课，是培养造就高层次专门人才所需数学素质的基本课程。它在培养和提高思维能力方面发挥着特有的作用，它的内容、思想、方法和语言已成为现代文化的重要组成部分。在让学生掌握基本理论与基本运算技能的基础上，要通过各个教学环节逐步培训学生的抽象概括能力、逻辑推理能力、空间想象能力和自学能力。在传授知识的同时，要着眼于提高学生的数学素质，培养学生用数学的方法去解决实际问题的意识、兴趣和能力。第一章函数与极限第一节映射与函数教学目的与要求：理解函数的概念，掌握函数的初等函数的性质及其图形，并会建立简单应用问题中的函数关系式。教学重点（难点）：理解复合函数及

3、分段函数，反函数及隐函数的概念，基本初等函数的性质及其图形。一、集合1、集合概念具有某种特定性质的事物的总体叫做集合。组成这个集合的事物称为该集合的元素。表示方法：用A，B，C，D 表示集合；用a，b，c，d 表示集合中的元素。1),321aaaA2)PxxA的性质元素与集合的关系：Aa，Aa一个集合，若它只含有有限个元素，则称为有限集；不是有限集的集合称为无限集。常见的数集：N，Z，Q，R，N+元素与集合的关系：A、B 是两个集合，如果集合A 的元素都是集合B 的元素，则称A是 B 的子集，记作BA。如果集合 A 与集合 B 互为子集，则称A 与 B 相等，记作BA若作BA且BA则称 A 是

4、 B 的真子集。全集 I：AiI（I=1，2，3，.）。空集：A。2、集合的运算并集BA：Ax|xBABx或交集BA：Ax|xBABx且差集BA：|BxAxxBA且补集（余集）CA：IA 集合的并、交、余运算满足下列法则：交换律：ABBAABBA文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2

5、Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E

6、9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2

7、H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10

8、K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T

9、1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2

10、I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3结合律：)()(C

11、BACBA，)()(CBACBA分配律：)()()(CBCACBA，)()()(CBCACBA对偶律：(cccBABA)cccBABA)(笛卡儿积：AB|),(ByAxyx且3、区间和邻域1）有限区间：开区间),(ba，闭区间ba,，半开半闭区间baba,。2）无限区间：（,a），,a，,a，,a，,。3）邻域：),(axaxaU注：a 邻域的中心，邻域的半径；去心邻域记为),(aU。二、映射定义设 X，Y 是两个非空集合，如果存在一个法则f，使得对 X 中的每一个元素x，按法则f，在 Y 中有唯一确定的元素y与之对应，则称f为从 X 到 Y 的映射，记作YXf：其中y称为元素x的像，并记作)

12、(xf，即)(xfy。注意：每个X 有唯一的像；每个Y 的原像不唯一。三、函数1、函数的概念定义设数集RD，则称映射RDf:为定义在D上的函数，记为Dxxfy,)(。注：函数相等：定义域、对应法则相等。2、函数的几种特性1）函数的有界性（上界、下界；有界、无界），有界的充要条件：既有上界又有下界。2）函数的单调性（单增、单减），在 x1、x2点比较函数值)(1xf与)(2xf的大小（注：与区间有关）。3）函数的奇偶性(定义域对称、)(xf与)(xf关系决定)，图形特点(关于原点、Y 轴对称)。4)函数的周期性(定义域中成立：)()(xflxf)3、函数与复合函数文档编

13、码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O

14、5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2

15、 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文

16、档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z

17、5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9

18、J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H

19、3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H31）反函数：函数)(:DfDf是单射，则有逆映射xyf)(1，称此映射1f为f函数的反函数。函数与反函数的图像关xy于对称。2）复合函数：函数)(ygu定义域为D1，函数)(xfy在 D 上有定义、且1)(DDf。则)()(xfgxfgu为复合函数。3）分段函数：分段函

20、数的统一表达式。结论：对于分段函数f（x）=12()()()()fxxafxxa若初等数函f1（x）和 f2（x）满足 f1（a）=f2（a），则f（x）=f112（x+a-2()xa）+f112（x+a+2()xa）-f1（a）4、初等函数1）幂函数：axy2)指数函数：xay3)对数函数：)(logxya4)三角函数：)cot(),tan(),cos(),sin(xyxyxyxy5)反三角函数：)arcsin(xy，)arccos(xy)cot()arctan(xarcyxy以上五种函数为基本初等函数。例1已知分段函数22,10,()1,0,2,01.xxf xxxx1）求其定义域并作图；

21、2）求函数值1122(),(0),().fff例2求由所给函数复合的函数，并求各复合函数的定义域：y=10u，u=1+x2,y=arctanu2,u=tanv,v=a2+x2.例3求函数的反函数及反函数的定义域：y=x2,（0 x0 为生产一个单位产品所需的可变成本。5.总收益(总收入)函数总收益 R 是指产品出售后，所得到的全部收入。它是销量Q 的函数，记为R(Q)。(通常假设产销平衡)若产品的单位售价p 不变，则R(Q)=pQ若价格 p 是产量 Q 的单调减少函数p(Q),则R(Q)=p(Q)Q 文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:C

22、O9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 H

23、X5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR

24、7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码

25、:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5

26、 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2

27、ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档

28、编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H36.总利润函数利润是生产中获得的总收益与投入的总成本之差。即产销平衡时，L(Q)=R(Q)-C(Q)7.库存润函数设某企业在计划期T 内，对某种物品总需求量为Q，由于库存费用及资金占用等因素，显然一次进货是不划算的，考虑均匀的分n 次进货，每次进货批量为Qqn，进货周期为Ttn.假定每件物品的贮存单位时间费用为1C，每次进货费用为2C，每次进货量相同，进货

29、间隔时间不变，以匀速消耗贮存物品，则平均库存为2q，在时间T 内的总费用E为1212QEC TqCq112C Tq其中，为储存费2QCq，为进货费用。第 3、4 讲章节次数第 3、4 讲：1.2 数列的极限教学目的要求1.了解数列极限的概念，性质。2.会用极限的分析定义证明一些简单的极限。主要内容数列、数列极限的定义与几何意义数列极限唯一性及收敛数列的有界性重点难点极限的概念的理解及应用；教学方法以讲授为主课后作业练习作业：第 3、4 讲：30 页的习题1、3 备注函数极限的基本性质同数列极限的性质。第二节数列的极限教学目的与要求：理解极限的概念，性质。教学重点（难点）：极限的概念的理解及应用

30、。一、数列数列就是由数组成的序列。1）这个序列中的每个数都编了号。文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5

31、O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B

32、4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:C

33、O9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 H

34、X5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR

35、7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码

36、:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H32）序列中有无限多个成员。一般写成：nxxxx321缩写为nx例 1 数列n1是这样一个数列nx，其中nxn1，5,4,3,2,1n也可写为：514131211可发现：这个数列有个趋势，数值越来越小

37、，无限接近0，记为01limnn。极限的N定义0，N，当Nn时，axn恒成立，则称数列nx的极限为a，记成axnnlim极限是数列中数的变化总趋势，因此与数列中某个、前几个的值没有关系。二、收敛数列的性质定理 1 如果数列nx收敛，那么它的极限是唯一。定理 2 如果数列nx收敛，那么数列nx一定有界。定理3 如果axnxlim且a0(a0，当nN时，)0(0nnxx。例2证明数列1nn的极限是1。例3作出数列1(1)nnn图形，讨论其极限值。微积分教案：第5、6 讲章节次数第 5、6 讲：1.3 函数的极限教学目的要求1.了解函数极限的概念，性质。2.会用极限的分析定义证明一些简单的极限。

38、3.理解函数左极限与右极限的概念，以及极限存在与左、右极限之间的关系。文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 H

39、X5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR

40、7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码

41、:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5

42、 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2

43、ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档

44、编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3主要内容自变量趋于无穷大及趋于有限数时函数的极限函数极限的几何解释单侧极限重点难点理解函数左极限与右极限，极限性质。教学方法讲授，练习，讨论课堂练习38 页的 1、2、3 课后作业38 页的 4

45、、5、6，补充分段函数求解极限的习题。备注函数极限的基本性质同数列极限的性质。第三节函数的极限教学目的与要求：理解函数左极限与右极限的概念，以及极限存在与左、右极限之间的关系。教学重点（难点）：理解函数左极限与右极限，极限性质。极限的定义一、在0 x点的极限1）0 x可在函数的定义域内，也可不在，不涉及f在0 x有没有定义，以及函数值)(0 xf的大小。只要满足：存在某个0使：Dxxxx),(),(0000。2）如果自变量x趋于0 x时，相应的函数值)(xf有一个总趋势以某个实数A为极限，则记为：Axfxx)(lim0。形式定义为：0，0，当00 xx时，Axf)(恒成立。ccxxxxfxfx

46、xxxxx000limlimlim00，记住：点是否有定义无关）在（）是否存在与（强调：文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L1

47、0K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3

48、T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A

49、2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9

50、L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5O3T1E9J2 ZR7B4A2I2H3文档编码:CO9L10K2Z5O5 HX5

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关键词：: 2022年教案第一章函数与极限 2022 教案第一章函数极限

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