2. In your solution, you must write your answers in exact form and not as decimal approximations. Consider the function
f(x) = e Ā²Ā², 2 xā¬R.
(a) Determine the fourth order Maclaurin polynomial Pā(x) for f.
(b) Using P(x), approximate e1/s.
(c) Using Taylor's theorem, find a rational upper bound for the error in the approximation in part (b).
(d) Using P(x), approximate the definite integral
1
ā« x2/e2 dx
0
(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. dx.
