I. Function, Limit and Continuity

Examination content

Concepts and representations of boundedness, monotonicity, periodicity and parity of functions

Properties and figures of basic elementary functions of sex inverse function, composite function and implicit function

The establishment of function relation in the simple application of elementary function: the limit of sequence and function

The definition of limit and the left and right limits of its property function are infinitesimal.

Four operational limits of infinity and infinitesimal comparison two criteria for the existence of limits: simplicity

Two important boundaries of adjusting bounded criterion and pinch criterion: (omitted)

The concept of continuous function, the types of discontinuous points of function, and the continuous closed domain of elementary function

Properties of Intermittent Continuous Functions (Maximum Theorem, Minimum Theorem and Intermediate Theorem)

Examination requirements

1. Understand the concept of function and master the representation method of function.

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

3. Understand the concept of composite function and the concepts of inverse function and implicit function.

4. Master the nature and graphics of basic elementary functions.

5. The functional relationship in simple application problems will be established.

6. Understand the concept of limit, the concept of left and right limit of function and the existence of limit.

The relationship between left and right limits.

7. Master the nature of limit and four algorithms.

8. Grasp the two standards of limit existence, and use them to seek the limit and grasp the benefits.

The method of finding the limit with two important limits.

9. To understand the concepts of infinitesimal, infinitesimal and infinitesimal order, we use equivalent nothing.

The poor seek the limit.

10. If you understand the concept of function continuity, you can identify the type of function discontinuity.

1 1. Understand the continuity of elementary functions and the properties of continuous functions on closed intervals (most

Maximum value, minimum value theorem, intermediate value theorem), and these properties will be applied.

Second, the differential calculus of unary function

Examination content

The concepts of derivative and differential, the geometric meaning and physical meaning of derivative can be

The relationship between the derivative of tangent and normal of plane curve and continuity basic elementary function

The derivative of a number and the four operations of differential inverse function, composite function and implicit function are all based on.

However, the concept of higher derivative of differential method of function determined by parametric equation is somewhat simple.

N-order derivative of function and invariant differential of first-order differential form in approximate calculation

Application of Rolle Theorem and Lagrange Mean Value Theorem to Cauchy

(Cauchy) Mean Value Theorem Taylor Theorem L'H?pital Method

Then the extreme value of the function and its solution are judged by the increase or decrease of the function and the concavity and convexity of the function graph.

The inflection point of definite function graph and its solution asymptote describes the graphic function of function.

Solution of Maximum and Minimum Value and Its Simple Application Concept and Calculation of Arc Differential Curvature

Dichotomy and tangent method for approximate solution of intersection angle equation of two curves with curvature radius