Consider the exponential function f(x) = exp(x). a) Calculate by hand the nth -order Maclaurin polynomial (Taylor polynomial about Xo-0) approximation of f(x) for n 0, 1, 2, 3, 4 and thus convince yourself that the Maclaurin series expansion of the exponential function is: Me k=0. k! b) Write a Matlab script (or function) that calculates the nth -order Maclaurin polynomial of f(x) according to formula (2.1) for an arbitrary order n. c) Consider the interval 0 sx s 2 and plot f(x), and its nth -order Maclaurin polynomial approximations for n = 0, 1, 2, 3, 4 in a single plot. Label the axes of your plot, and use a legend to identify the different curves. d) Using the plot in part c), explain what happens with the nth-order Maclaurin polynomials as n increases. Hint: You may use symbolic computation and Matlab built-in functions taylor and ezplot