例3讨论x→0时,f(x)=|x|的极限是否存在? 解:f(x)=x xx≥0 x x<0 因为x=0是函数(x)的分界点,故 lim f(x)=lim(x)=0 x->0 x→>0 lim f(x)=limx=0 x→>0 即:limf(x)=limf(x)=0 x->0 →0 所以 lim f(x)=o x→0 Economic-mathematics 16-16 Wednesday, February 24, 2021Economic-mathematics 16 - 16 Wednesday, February 24, 2021 例3 讨论x→0时，f(x)=∣x∣的极限是否存在？ 解：    −   = = 0 0 ( ) x x x x f x x 因为x=0是函数f(x) 的分界点，故 ( ) 0 ( ) ( ) 0 lim lim lim lim 0 0 0 0 = = = − = + + − − → → → → f x x f x x x x x x 即： ( ) ( ) 0 lim lim 0 0 = = → − → + f x f x x x 所以 ( ) 0 lim 0 = → f x x