单侧连续 左连续:limf(x)=f(x0) x→>x f∫(x0-0)=f(x0)f(x)=f(x) 右连续:limf(x)=f(x0 x-x f(x+0)=f(x)f(x0+)=f(x) October 2004
October, 2004 单侧连续 左连续 ： 0 0 lim ( ) ( ) x x f x f x → − = 0 0 f x f x ( 0) ( ) − = 0 0 f x f x ( ) ( ) − = 右连续 ： 0 0 lim ( ) ( ) x x f x f x → + = 0 0 f x f x ( 0) ( ) + = 0 0 f x f x ( ) ( ) + =
f(x f(x) f(x): f(o) : f(x) f(x):f(ro): f(x) X 0 X 左连续但不右连续右连续但不左连续 October 2004
October, 2004 0 x x f x( )f x( ) f x( ) x f x( ) 0 f x( ) 0 x x f x( )f x( ) f x( ) x f x( ) 0 f x( ) 左连续但不右连续 右连续但不左连续
函数f(x)在点x处连续的充分必要条件是: fx)在点x既左连续,又右连续。 limf(x)=f(x0)分 x->x0 lim f(x=f(ro)=lim f(x) x→>x f(x) f(x):f(o) :f(x) X X October 2004
October, 2004 函数 f(x) 在点 x0 处连续的充分必要条件是： f(x) 在点 x0 既左连续，又右连续。 0 0 lim ( ) ( ) x x f x f x → = 0 0 lim ( ) ( ) x x f x f x → − = 0 lim ( ) x x f x → + = 0 x x f x( )f x( ) f x( ) x f x( ) 0 f x( )