(a) Compute the 2nd, 3rd, and 4th order Taylor approximation of the following functions about the point xo = 0. Also bound the error of approximation at x = 3. ii) sin.x (b) Let us say we would like an accurate polynomial approximation of the functions in part (a) for all x 6 [-3.3). In other words, we want a polynomial of degree D (call it op) such that If(x) -op(x)| ,f]. Write the 3rd order Taylor expansion of f(x()) for the variable / about the point fo = 0. Use the chain rule. (f) Similar to part (b), determine the degree D for the polynomial op(x()) from the Taylor series about the point fo = 0 such that If(3()) - op(x())|