Let f(x) = In(2 - x), a = 1,b = 1.9 a) Find the linear, quadratic, and cubic Taylor polynomials around the point : = a). You may use Mathematica for intermediate steps only (for example, for calucalting derivatives of the function). b) Graph the original function f(a) and all Taylor polynomials from the step a) on the same set of axes. c) What is the purpose of Taylor polynomials? d) What happens as the degree of Taylor polynomial increases? Are your explanations supported by the graph from b) ? e) Using the quadratic or cubic (your choice) Taylor polynomial, approximate f(b) with 8 significant digits and compare it with the actual value of f(b). Calculate the relative error percentage in approximationg f(b) by the chosen Taylor polynomial. f) For the chosen at the previous step Taylor polynomial, find the remainder term, R2 (b) or R; (b) with 8 significant digits. g) Which part on your graph represents the remainder term? If needed, you can sketch your graph on the paper to indicate the remainder part. Find theoretical bounds of the error for the chosen Taylor polynomial. O Compare your computation results form f) with the theoretical results from h). Do your computational results upport your theoretical calculations