目录一、函数与极限·······························································································21、集合的概念····························································································22、常量与变量····························································································32、函数·····································································································43、函数的简单性态······················································································44、反函数··································································································55、复合函数·······························································································66、初等函数·······························································································67、双曲函数及反双曲函数·············································································78、数列的极限····························································································89、函数的极限····························································································910、函数极限的运算规则············································································11一、函数与极限1、集合的概念一般地我们把研究对象统称为元素，把一些元素组成的总体叫集合（简称集）。集合具有确定性（给定集合的元素必须是确定的）和互异性（给定集合中的元素是互不相同的）。比如“身材较高的人”不能构成集合，因为它的元素不是确定的。我们通常用大字拉丁字母A、B、C、⋯⋯表示集合，用小写拉丁字母a、b、c⋯⋯表示集合中的元素。如果a是集合A中的元素，就说a属于A，记作：a∈A，否则就说a不属于A，记作：aA。⑴、全体非负整数组成的集合叫做非负整数集（或自然数集）。记作N⑵、所有正整数组成的集合叫做正整数集。记作N+或N+。⑶、全体整数组成的集合叫做整数集。记作Z。⑷、全体有理数组成的集合叫做有理数集。记作Q。⑸、全体实数组成的集合叫做实数集。记作R。集合的表示方法⑴、列举法：把集合的元素一一列举出来，并用“｛｝”括起来表示集合⑵、描述法：用集合所有元素的共同特征来表示集合。集合间的基本关系⑴、子集：一般地，对于两个集合A、B，如果集合A中的任意一个元素都是集合B的元素，我们就说A、B有包含关系，称集合A为集合B的子集，记作AB（或BA）。。⑵相等：如何集合A是集合B的子集，且集合B...
