1. Assume a continuous function f(x) defined on a axis with a uniform grid of spacing h. Using appropriate Taylor Series expansions, find the leading order truncation term (L.O.T. ) in the following approximate formulae for the first or second derivatives given below. Clearly indicate the order of accuracy of the approximation. Note that the sign of the L.O.T. is based on the term being on the right-hand side of the expansion for the above formulae. (a) f' ( x) ~ f (x + 2h) + of(x + h) - of(x - h)+f(x-2h) 12h (1) (b) f'(x ) ~ _ -11f(x) + 18f(x + h) - 9f (x + 2h) + 2f(x + 3h) 6h ( 2 ) (C ) f'(x) ~ J(x - 2h) - 4f(x - h) + 3f(2) 2h (3) (d) f"(x) ~-f(x -2h) + 16f(x-h) - 30f(x) + 16f(x th) - f(x + 2h) 12h2 ( 4)