Corollary 1. 2(Newton Approximation). Assume that PN(a)is the New- ton polynomial given in Theorem 1.5 and is used to approximate the function f(a), that is, f(a)=PN(ar)+ en(c) If f E CN+a, b, then for each r E a, b] there corresponds a number c= c(a) in (a, 6), so that the error term has the form EN(a) T-70x-21)…(x-xN)代(N+1)(C (N+1)!