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For a given function f whose (n−1)^th derivative is continuous in [a,b] and whose n^th derivative exists in (a,b), we can write f(x+a) as a Taylor series ie:

f(x+a)=f(a)+f′(a)x+f"(a)x2/2+f"′(a)x3/3!+... +f(n−1)(a)xn−1/(n−1)!+Rn.

(x+a must lie in [a,b].) Rⁿ is a remainder term; it can be written in various forms; its value is usually small.