The Second Outline of Mathematics for Postgraduate Entrance Examination is a book published by Higher Education Press on 20 13. The author is the editorial board of the national unified postgraduate counseling book. This book is an analysis of the second national unified postgraduate entrance examination outline for mathematics. It is applicable to all the secondary mathematics entrance exams after 20 13, and the outline will not be changed.

Function, limit, continuity

Examination content

The concept and expression of function: boundedness, monotonicity, periodicity and parity of function, properties of composite function, inverse function, piecewise function and implicit function, and the establishment of functional relationship of graphic elementary function. The definitions of sequence limit and function limit, left limit and right limit of property function, the concepts of infinitesimal and infinitesimal and their relationship, four operational limits of infinitesimal comparison limit, and two important limits: monotone boundedness criterion and pinch criterion;

Concept of Function Continuity Types of Discontinuous Points of Functions Continuity of Elementary Functions Properties of Continuous Functions on Closed Interval

Examination requirements

1. Understand the concept of function and master the expression of function, and you will establish the functional relationship of application problems.

2. Understand the boundedness, monotonicity, periodicity and parity of functions.

3. Understand the concepts of compound function and piecewise function, and the concepts of inverse function and implicit function.

4. Grasp the nature and graphics of basic elementary functions and understand the concept of elementary functions.

5. Understand the concept of limit, the concept of left and right limit of function and the relationship between the existence of function limit and left and right limit.

6. Master the nature of limit and four algorithms.

7. Master two criteria for the existence of limit, and use them to find the limit, and master the method of using two important limits to find the limit.

8. Understand the concepts of infinitesimal and infinitesimal, master the comparison method of infinitesimal, and find the limit with equivalent infinitesimal.

9. Understanding the concept of function continuity (including left continuity and right continuity) will distinguish the types of function discontinuity points.

10. Understand the properties of continuous function and continuity of elementary function, understand the properties of continuous function on closed interval (boundedness, maximum theorem, mean value theorem), and apply these properties.