The following is an example of a third-order accurate forward-difference method for the first derivative, f 0 (x) = − 11 6 f(x) + 3f(x + h) − 3 2 f(x + 2h) + 1 3 f(x + 3h) h + o(h 3 ).
(1) assume that the error in calculating f 0 (a) at the point x = a with h = 0.2 is exactly 2 × 10−6 . which of the following is most true? save your answer to a10.dat.
a the error for calculating f 0 (a) with h = 0.02 is exactly 2 × 10−3 .
b the error for calculating f 0 (a) with h = 0.02 is approximately 2 × 10−3 .
c the error for calculating f 0 (a) with h = 0.02 is exactly 8 × 10−6 .
d the error for calculating f 0 (a) with h = 0.02 is approximately 8 × 10−6 .
e the error for calculating f 0 (a) with h = 0.02 is exactly 2 × 10−7 .
f the error for calculating f 0 (a) with h = 0.02 is approximate 2 × 10−7 .
g the error for calculating f 0 (a) with h = 0.02 is exactly 2 × 10−9 .
h the error for calculating f 0 (a) with h = 0.02 is approximately 2 × 10−9 .