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 functions and the continuity of elementary functions. 1. Understand the properties of continuous functions on closed intervals (boundedness, maximum theorem, mean value theorem) and apply these properties.

Univariate differential function

Examination requirements

1. Understand the concepts of derivative and differential, understand the relationship between derivative and differential, understand the geometric meaning of derivative, find the tangent equation and normal equation of plane curve, understand the physical meaning of derivative, describe some physical quantities with derivative, and understand the relationship between function derivability and continuity.

2. Master the four algorithms of derivative and the derivative rule of compound function, and master the derivative formula of basic elementary function. Knowing the four algorithms of differential and the invariance of first-order differential form, we can find the differential of function.

3. If you understand the concept of higher derivative, you will find the higher derivative of simple function.

4. We can find the derivative of piecewise function, implicit function, function determined by parametric equation and inverse function.

5. Understand and apply Rolle theorem, Lagrange mean value theorem, Taylor theorem, and Cauchy mean value theorem.

6. Master the method of finding the limit of infinitive with L'H?pital's law.

7. Understand the concept of extreme value of function, master the method of judging monotonicity of function and finding extreme value of function with derivative, and master the method of finding maximum and minimum value of function and its application.

8. Will judge the concavity and convexity of the function graph by derivative (note: in the interval (a, b), let the function f(x) have the second derivative. When f'' (x) >; =0, the graph of f(x) is concave; When f'' (x)