高等数学英文1-2-10.ppt

1、Chapter 1Functions and Limits,1.2 Functions,I. Functions,1. Definition,A function f is a rule of correspondence that associates with each object x in one set and a single value y from a second set.,Domain Range independent variable dependent variable,f,Q: how to find the domain of a function?,Q: how

2、 to discriminate two functions are the same?,Find the circumference of a polygon with n equal sides that is inscribed to a circle with radius r.,I. Functions,1. Definition,2. Special Functions,Greatest integer function,= the greatest integer less than or equal to x.,Sign function,I. Functions,II. Pr

3、operties of Functions,1. Boundedness,II. Properties of Functions,1. Boundedness,We say f (x) is bounded on X if,2. Monotonicity,then f is increasing on X if,f is decreasing on X if,Def:,For example,II. Properties of Functions,II. Properties of Functions,3. Odd and even functions,For example,4. Perio

4、dic functions,III. Inverse Functions,The graphs of f and are symmetric with line y =x.,If f is a monotonic function, then so is,IV. Composite Functions,is called the composition of f with g.,For example:,V. Elementary Functions,1. Basic Elementary Functions,Power Function,V. Elementary Functions,1.

5、Basic Elementary Functions,Exponential Function,V. Elementary Functions,1. Basic Elementary Functions,Logarithmic Function,V. Elementary Functions,1. Basic Elementary Functions,Trigonometric Functions,V. Elementary Functions,1. Basic Elementary Functions,Trigonometric Functions,V. Elementary Functio

6、ns,1. Basic Elementary Functions,Trigonometric Functions,V. Elementary Functions,1. Basic Elementary Functions,Inverse Trigonometric Functions,V. Elementary Functions,1. Basic Elementary Functions,Inverse Trigonometric Functions,V. Elementary Functions,2. Elementary Functions,Def: A composite function that is obtained from operations on or composed by basic elementary functions.,For example:,Class exercises,Sketch the grap