证:limf(x)=f(x) x->x0 lim g(x)=g(xo) x->x0 limf(x)+g(x)=lim f(x+lim g(x) x→>x0 x->0 x-0 =f(x0)+g(x0 所以f(x)+g(x)在点x0处连续。 October 2004October, 2004 证 0 0 lim ( ) ( ) x x f x f x → = 0 0 lim ( ) ( ) x x g x g x → = 0 lim[ ( ) ( )] x x f x g x →  + 0 0 lim ( ) lim ( ) x x f x g x → → = + 0 0 = + f x g x ( ) ( ) 所以 f x g x ( ) ( ) + 在点 x0 处连续