vault backup: 2026-04-08 10:52:57

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考研/math/002_第1讲.md

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 <table><tr><td>考题</td><td>计算函数极限</td></tr><tr><td>题型</td><td>选择题、填空题、解答题 ①理解函数的概念，掌握函数的表示法，会建立应用问题的函数关系；</td></tr><tr><td>目标</td><td>②了解函数的有界性、单调性、周期性和奇偶性； ③理解复合函数及分段函数的概念，了解反函数及隐函数的概念； ④掌握基本初等函数的性质及其图形，了解初等函数的概念； ⑤理解极限的概念，理解函数左极限与右极限的概念以及函数极限存在与左极限、右极限之间的关系； ③掌握极限的性质及四则运算法则，掌握利用两个重要极限求极限的方法； ⑦掌握极限存在的两个准则，并会利用它们求极限（仅数学一、数学二），了解极限的性质及 极限存在的两个准则（仅数学三）； ③理解无穷小量、无穷大量的概念，掌握无穷小量的比较方法，会用等价无穷小量求极限； ③理解函数连续性的概念（含左连续与右连续），会判别函数间断点的类型；</td></tr><tr><td>重难点</td><td>10了解连续函数的性质和初等函数的连续性 ①洛必达法则；②泰勒公式</td></tr></table>
 
 按《全国硕士研究生招生考试数学考试大纲》来编写的基础知识结构，只不过我把大纲中罗列的知识点做成了一个体系化的知识结构图，希望同学们每学宅一讲，回过头来能够自己写出基础知识结构.
-
-![](images/0ed1c9c5be526a658e2eb3eaceac6634fd093a36ef7421d305c875ea3ab5156a.jpg)
-
 ## 基础知识结构
 
 ![](images/231927b26a8191d3226a4ba96b6f945dcbcebdb87d8e6d811b741636683c0670.jpg)
@@ -24,16 +21,16 @@
 ![](images/74a100db082d274876e036335671f14987584bf05452ab58d09a168c36f791ab.jpg)
 
 ## 函数的概念与特性
+![[27张宇基础30讲高数.pdf#page=11&rect=144,533,291,628|27张宇基础30讲高数, p.11]]
 
 ![](images/e89058068960f0d960b6817ae94b089b8823c71b8977d391e32ba0a7edf88ef1.jpg)
 
 ## 1函数
-
 设x与y是两个变量，D是一个给定的数集，若对于每一个x∈D，按照一定的法则f，有一个确定的y值与之对应，则称y为x的函数，记作y=f(x)，称x为自变量，y为因变量，称数集D为此函数的定义域，定义域一般由实际背景中变量的具体意义或者函数对应法则的要求确定，称 $\{ f ( x ) { \big \vert } x \in D \}$ 为值域.
 
 ## 注单值函数与多值函数
 
-事实上，上述定义的函数是单值函数，若给一个 $x _ { 1 }$ ，对应一个 $y _ { 1 }$ ；给另外一个 $x _ { 2 }$ ，对应另外一个$y _ { 2 }$ ，这叫一对一[见图1-1(a)].若给定 $x _ { 1 } \ : , \ : x _ { 2 } \ : ( \ : x _ { 1 } \neq x _ { 2 } )$ ，它们对应同一个y，则称多对一[见图1-1(b)]，所以函数可以一对一，也可以多对一，这叫单值函数。
+事实上，上述定义的函数是单值函数，若给一个 $x _ { 1 }$ ，对应一个 $y _ { 1 }$ ；给另外一个 $x _ { 2 }$ ，对应另外一个$y _ { 2 }$ ，这叫一对一[见图1-1(a)].若给定 $x _ { 1 }  ,  x _ { 2 } ( \ : x _ { 1 } \neq x _ { 2 } )$ ，它们对应同一个y，则称多对一[见图1-1(b)]，所以函数可以一对一，也可以多对一，这叫单值函数。
 
 但是，若一个x对应一个 $y _ { 1 }$ ，又对应另一个 $y _ { 2 }$ ，也就是一对多，这叫多值函数[见图1-1(c)]，它不在上述定义中