Use Richardson extrapolation to find an improved estimate for the first derivative of y = cos x at x =π/4 using step sizes of h1 = π/3 and h2 = π/6. Employ centered differences of O(h2) for the...

Use Richardson extrapolation to find an improved estimate for the first derivative of y = cos x at x =π/4 using step sizes of h1 = π/3 and h2 = π/6. Employ centered differences of O(h2) for the initial estimates. Discuss from your results the effect of using Richardson extrapolation on the error of using centered differences.