《高等数学》课程电子教案（PPT课件）Chapter 1 Functions and Limits §1.3 The Limits of Functions

I.Intuitive Meaning ofLimit2x2 - 2Consider the function: f(x) =x-1When x±1, f(x)-4=2x-1台x-1<0.052x-1<0.1 xS 1.3 The Limits of functions

§1.3 The Limits of functions I. Intuitive Meaning of Limit f (x) − 4 = 2 x −1  x −1  0.05 y o x 4 1 Consider the function: , 1 2 2 ( ) 2 − − = x x f x When x  1, 2 x −1  0.1

I.Intuitive Meaning of Limit2x2 -2Consider the function: f(x) =x-12When x±1, f(x)-4= 2x-12x-1<0.052x-1 <0.12|x -1| <0.01 |x -1 <0.005x12x-1 < 0.001 |x-1|<0.0005We usethe Greek letter to stand for arbitrarypositive numberD2x-1<8x-1<2S1.3 The Limitsof functions

§1.3 The Limits of functions I. Intuitive Meaning of Limit f (x) − 4 = 2 x −1  x −1  0.05 2 x −1   2 1   x −  y o x 4 1 Consider the function: , 1 2 2 ( ) 2 − − = x x f x When x  1, 2 x −1  0.1 2 x −1  0.01  x −1  0.005 2 x −1  0.001  x −1  0.0005 We use the Greek letter to stand for arbitrary positive number  2 x −1  