7.4 Series Expansions

. Series Expansions Taylor’s series and Maclaurin's series expansion of a function which are infinitely differentiable. Theorem . (a) Taylor’s Series Let f x ( ) be a function infinitely differentiable at x . Then f x ( ) can be expanded as a series, in an interval ( ), - e e e > , of the form ( ) = f a ! ! ! ∞