CONTENTS Introduction 3
Section I. FUNCTIONS AND LIMITS
Chapter 1. Repetition and deepening of basic information about functions and properties of functions 6
§ 1. Repetition of the concept of a function. Function graph. General notation of a function 6
§ 2. Monotone functions. Increase and decrease of a function on a given interval. The concept of the maximum and minimum of a function 11
§ 3. Even and odd functions. Top-bounded and bottom-bounded functions. Limited features. Periodic functions. Scheme of investigation of a function 15
Chapter 2. Inverse functions 23
§ 1. The concept of an inverse function. Graph of an inverse function 23
§ 2. Properties of inverse functions 27
§ 3. Inverse trigonometric functions 31
Chapter 3. Limit of a function 34
§ 1. Limit of the function f (x) as u oo 36
§ 2. Limit of the function f (x) as x - a (a is a real number) 48
§ 3. Limit of the ratio of the sine to the argument when the argument tends to zero 56
§ 4. Theorems on limits 61
§ 5. The concept of continuity of a function 67
Section II. THE DERIVATIVE AND ITS APPLICATION
Chapter 4. The concept of the derivative. Calculation of the derivative. Application of the derivative to the solution of physical and other problems 75
§ 1. The speed of rectilinear motion. The concept of a derivative 76
§ 2. Theorems on derivatives. Derivatives of some elementary functions 82
§ 3. Physical and other examples of the use of the derivative
Acceleration. The concept of the second derivative 101
Chapter 5. Geometric meaning of the derivative. Exploring functions using a derivative. Solving problems related to finding the largest and smallest values of functions. Newton binomial formula 112
§ 1. Geometric meaning of the derivative 113
§ 2. Study of functions for increasing and decreasing and finding the maximum and minimum points of functions using the derivative 125
§ 3. Study of functions using the derivative and the construction of their graphs. Graphical solution of equations 140
§ 4. Problems of finding the maximum and minimum values of functions 163
§ 5. Derivation of the Newton binomial formula and its application to approximate calculations 171
