证](1)用连续定义证明 任取x∈[a,b,x+Ax∈[a,b x+4r F(x+△)-F(x)=∫f(ot-jf(t x+Ax x+Ax =「f()df()=」f(r)dt ∫∈Ra,b→彐M>0,f(x)≤MVx∈a,b x+dl x+Ar 0sIF(x+dx)-F(x)=Sr(d Jr(dt ≤M4x→0(4x>0) 2021/2/202021/2/20 5 [证] (1) 用连续定义证明 任取 x[a, b], x +  x[a, b]   + − = − + x a x x a F(x x) F(x) f (t)dt f (t)dt     = + + a x x x a f (t)dt f (t)dt   + = x x x f t dt  ( ) f  R[a, b]  M  0, f (x)  M  x [a, b]   + +  + − =  x x x x x x F x x F x f t dt f t dt   0 (  ) ( ) ( ) ( )  M   x → 0 ( x → 0)