Theorem 1. 1(Taylor Polynomial Approximation). Assume that f E CN+ a, b ando∈[a, is a fixed value.fr∈[a,],then f(a)=PN(a)+ en(c), where PN(a)is a polynomial that can be used to approximate f(ar) f()≈()=∑ N f()(ro) k! -0 (1.2) The error term EN(a) has the form (N+1 EN(a) (N+1)! for some value c=c(a) that lies between r and To