考研数学经典实用基础知识点及例题演示(超值强化).pdf

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1、目录一、函数与极限·························································································21、集合的概念··························································································22、常量与变量··················································

2、········································32、函数···································································································43、函数的简单性态·····················································································44、反函数·········

3、·······················································································55、复合函数·····························································································66、初等函数····························································

4、·································67、双曲函数及反双曲函数············································································78、数列的极限··························································································89、函数的极限··························

5、································································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

6、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：aA。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N+⑵、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⑵
、列举法：把集合的

7、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AB（或BA）。。⑵相等：如何集合A是集合B的子集，且集合B是集合A的子集，此时集合A中的元素与集合B中的元素完全一样，因此集合A与集合B相等，记作A＝B。⑶、真子集：如何集合A是集合B的子集，但存在一个元素属于B但不属于A，我们称集合A是集合B的真子集。⑷、

8、空集：我们把不含任何元素的集合叫做空集。记作，并规定，空集是任何集合的子集。⑸、由上述集合之间的基本关系，可以得到下面的结论：①、任何一个集合是它本身的子集。即AA②、对于集合A、B、C，如果A是B的子集，B是C的子集，则A是C的子集。③、我们可以把相等的集合叫做“等集”，这样的话子集包括“真子集”和“等集”。集合的基本运算⑴、并集：一般地，由所有属于集合A或属于集合B的元素组成的集合称为A与B的并集。记作A∪B。（在求并集时，它们的公