- #1
irishetalon00
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Homework Statement
(See attachment: if it doesn't work, see below for poorer formatting)[/B]
Theorem 6.1 (Centered Formula of Order O(h2)). Assume that f ∈ C^3[a, b] and that x − h, x, x + h ∈ [a, b]. Then (3) f (x) ≈ f (x + h) − f (x − h) 2h . Furthermore, there exists a number c = c(x) ∈ [a, b] such that (4) f (x) = f (x + h) − f (x − h) 2h + Etrunc( f, h), where Etrunc( f, h) = −h2 f (3) (c) 6 = O(h2).
Homework Equations
While reading Theroem 6.1, I have difficulty understanding (realms? "∈") in general, so I was wondering what is meant by C^3