Answer Happy

EE2E11-1 4. An engineer wishes to investigate the impact of different finite difference ap- proximations for derivatives of the function f(x) = -x+exp(-2x) (a) Using an interval of Ax, write down the forward, backward and central finite difference approximations to the derivative of at x = x1 [10 marks] (b) Calculate the values of these three approximations at #₁ = 1.0, 2.5, using Ax=0.5. [5 marks] (c) Compare your approximations to the actual analytic derivative for this function. Using the Taylor series expansion, explain the size of the dis- crepancies you observe if any. Comment on how you could improve these kinds of finite difference approximations. [10 marks]