Let us numerically evaluate the derivative of f(x)= sin(x) at x=pi/3, using two different numerical formulae. Use Matlab to solve the problem.

11101. Let us numerically evaluate the derivative of f(c) = sin(x) at x = 1/3, using two different numerical formulae: Centered-difference formula: f'(z) = f(x + h) - f(x - h) 2h Forward-difference formula: f(x + h) - f(x) h (Vary the step-size h between 10-15 to 10-1 (consider using the logspace command), and construct a log-log plot of absolute error and h. Note that we can compute the absolute error, since we know that the true value of f'(T/3) = 0.5. Using the graphs above, Find a) the (approximately) optimum value of h for the two difference formula, and compare the absolute errors of the two numerical formulae. 11101. Let us numerically evaluate the derivative of f(c) = sin(x) at x = 1/3, using two different numerical formulae: Centered-difference formula: f'(z) = f(x + h) - f(x - h) 2h Forward-difference formula: f(x + h) - f(x) h (Vary the step-size h between 10-15 to 10-1 (consider using the logspace command), and construct a log-log plot of absolute error and h. Note that we can compute the absolute error, since we know that the true value of f'(T/3) = 0.5. Using the graphs above, Find a) the (approximately) optimum value of h for the two difference formula, and compare the absolute errors of the two numerical formulae