Repeat Example 13.18 using the central-difference formula of O(h⁴).

Example 13.18

Compute {D_hk f(x)} at x = 2 for the following functions. You should use step size h_k = 10^−k for k = 1, 2, . . . until an apparent convergence to five decimal places is observed.

f(x) = 0.7x

g(x) = ln(x)

k(x) = e^x

m(x) = cos(x)