Use octave and excel to solve the following problems.

The Maclaurin series expansion for the arctangent of x is defined for x S 1 as arctan x = 2n + 1 n=0 1 (-1) x2n+1 Using single precision arithmetic, calculate the approximate value of arctant /8 using 1, 2, 3, up to 50 terms. In each of the calculations, determine true and approximate relative errors. Discuss the convergence of the Maclaurin series in terms of the behavior of the errors obtained. Consider the function f(x) = x3 2x + 4 with x = -2,-1,0,1 2 and h = 0.25 initially. Use the forward, backward, and centered finite difference approximations for the first and second derivative of f(x) at given values for x. Compare the true relative errors of each method and at each value of x. d Consider also how the step size h affects the approximate value of the first and second derivatives. Use the step sizes 0.1, 0.05, 0.01, 0.005, and 0.001. Comment on the results. The Maclaurin series expansion for the arctangent of x is defined for x S 1 as arctan x = 2n + 1 n=0 1 (-1) x2n+1 Using single precision arithmetic, calculate the approximate value of arctant /8 using 1, 2, 3, up to 50 terms. In each of the calculations, determine true and approximate relative errors. Discuss the convergence of the Maclaurin series in terms of the behavior of the errors obtained. Consider the function f(x) = x3 2x + 4 with x = -2,-1,0,1 2 and h = 0.25 initially. Use the forward, backward, and centered finite difference approximations for the first and second derivative of f(x) at given values for x. Compare the true relative errors of each method and at each value of x. d Consider also how the step size h affects the approximate value of the first and second derivatives. Use the step sizes 0.1, 0.05, 0.01, 0.005, and 0.001. Comment on the results