In your solution, you must write your answers in exact form and not as decimal approximations. Consider the function f(x) = e², x ≤ R. (a) Determine the fourth order Maclaurin polynomial P₁(x) for f. (b) Using P₁(x), approximate es. (c) Using Taylor's theorem, find a rational upper bound for the error in the approximation in part (b). (d) Using P4(x), approximate the definite integral [ e 2 dx. (e) Using the MATLAB applet Taylortool: i. Sketch the tenth order Maclaurin polynomial for f in the interval −3 < x < 3. ii. Find the lowest degree of the Maclaurin polynomial such that no difference between the Maclaurin polynomial and f(x) is visible on Taylortool for x € (−–3, 3). Include a sketch of this polynomial. Page 1 of 2