A) Derive the central difference approximation for f"(x) accurate to O(h) by applying Richardson extrapolation to the central difference approximation of O(h2). B) Use the data in the table below to compute f (0.2) as accurately 0.1 0.2 0.3 0.4 f(x) 0.000 000 | 0.078 348 | 0.138 910 | 0.192916 | 0.244981 I.e. use Richardson extrapolation with central difference approximation (as in part A) C) Use the two approximations in A (the given and derived one) to estimate the second derivative of f(x-sin(x) + e-r at x = 0 using h = 0.1 and h = 0.5. What are the errors for each of the A) Derive the central difference approximation for f"(x) accurate to O(h) by applying Richardson extrapolation to the central difference approximation of O(h2). B) Use the data in the table below to compute f (0.2) as accurately 0.1 0.2 0.3 0.4 f(x) 0.000 000 | 0.078 348 | 0.138 910 | 0.192916 | 0.244981 I.e. use Richardson extrapolation with central difference approximation (as in part A) C) Use the two approximations in A (the given and derived one) to estimate the second derivative of f(x-sin(x) + e-r at x = 0 using h = 0.1 and h = 0.5. What are the errors for each of the