ABSTRACT
Substituting for a0,a1,a2, . . . in equation (1) gives:
f (x) = f (0)+ f ′(0)x + f ′′(0) 2!
+ f ′′′(0) 3!
x3 + · · ·
i.e. f(x) = f(0)+ xf ′(0)+ x
2! f ′′(0)
+ x 3
3! f ′′′(0)+·· ·
(5)
Equation (5) is a mathematical statement called Maclaurin’s theorem or Maclaurin’s series.
