cos(x) Compute f'(0.5), f'(0.2), (0.5), and f (0.2) for f(x) = () P3(x) to five...

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cos(x) Compute f'(0.5), f'(0.2), " (0.5), and f" (0.2) for f(x) = () P3(x) to five decimal place accuracy (by choosing an appropriate h value) using the central difference formulas: f(x + h) f(x h) f'(x)~ 2h and f" (x) = f(x+h)2f(x) + f(x h) h The derivative can be computed analytically, so you may wish to compare your result to the analytical solution. numerical : 1 1 Find the most accurate finite difference formula and the corresponding leading error term for the second derivative given the values of the function and its second derivative at xi, x-1, and x+1. Assume the points are uniformly spaced. analytical. use TS expansion cos(x) Compute f'(0.5), f'(0.2), " (0.5), and f" (0.2) for f(x) = () P3(x) to five decimal place accuracy (by choosing an appropriate h value) using the central difference formulas: f(x + h) f(x h) f'(x)~ 2h and f" (x) = f(x+h)2f(x) + f(x h) h The derivative can be computed analytically, so you may wish to compare your result to the analytical solution. numerical : 1 1 Find the most accurate finite difference formula and the corresponding leading error term for the second derivative given the values of the function and its second derivative at xi, x-1, and x+1. Assume the points are uniformly spaced. analytical. use TS expansion