Plot (x) = 1/(1 + x) together with the Taylor polynomials T n at a = 1 for 1 n 4 on the

Plot ƒ(x) = 1/(1 + x) together with the Taylor polynomials T_n at a = 1 for 1 ≤ n ≤ 4 on the interval [−2, 8] (be sure to limit the upper plot range).

(a) Over which interval does T4 appear to approximate ƒ closely?
(b) What happens for x < −1?
(c) Use your computer algebra system to produce and plot T₃₀ together with ƒ on [−2, 8]. Over which interval does T₃₀ appear to give a close approximation?