Recall Taylor's theorem from Calculus: "Assume a function f(a) that has k + 1 derivatives in an interval a, b, or simply, f E Ck+1 a, b] and , E a, b . Then, for very x E [a, b), 38 between To and x such that k f ( 2 ) = f (n) () f ( * +1) (8) + (ac - 20 0) K+1, (1) n! (k + 1)! PAT) ER() where PK(x) is called the kth Taylor polynomial for f around , and Ek(x) is called the remainder, or truncation error". Note that lim PK (a) gives the Taylor series for the same functionf about x = x, and also a function f is