4) Evaluate numerically the df/dx at x=0 for three f(x) functions of sin(x), cos(x) and ex with the following FD schemes: a) first-order accurate forward b) central second-order accurate c) central fourth-order accurate Vary Ax between 0.1 and 0.001 and plot in the logarithmic scale the error as a function of Ax. You should produce three plots, one for

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4) Evaluate numerically the df/dx at x=0 for three f(x) functions of sin(x), cos(x) and ex with the following FD schemes: a) first-order accurate forward b) central second-order accurate c) central fourth-order accurate Vary Ax between 0.1 and 0.001 and plot in the logarithmic scale the error as a function of Ax. You should produce three plots, one for each function. Each plot should have three curves, one for each discretization scheme. How can you deduce the order of accuracy of each discretization scheme from these plots? Explain what you observe in the plots.

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