1. Taylor Series and Function Calculation
Theorem 1.1 (Taylor Polynomial Approximation). Assume that f C N+1[a, b] and x0 [a, b] is a fixed value. If x [a, b] , then
f(x) = PN(x) + EN(x), (1.1)
where PN(x) is a polynomial that can be used to approximate f (x):