△u- Ou lim lim △y- Ov Ar-0△x Ox'Ar0△x 8x 又 lim△ux=0,lim△yx=0, △x→0 △x→>0 从而 lim p=0 △x-→0 所以，li o(p）=lim o()V(Au,)+(Av)2 x→0△X Ax-→0 △x =±lim =0 7 7 0 lim x x u u  → x x   =   , 0 lim x x v v  → x x   =   又 0 lim 0 x x u  →  = , 0 lim 0 x x v  →  = , 从而 0 lim 0 x   → = 所以, 2 2 0 0 ( ) ( ) ( ) ( ) lim lim[ ] x x x x o o u v x x    →  →   +  =   2 2 0 0 ( ) lim lim ( ) ( ) ] x x x x o u v x x   →  →    =  +   2 2 0 ( ) ( ) ] u v x x   =   +   = 0