Let f(x)=x1, and x0=5.
((a)) Find T2(x).
((b)) Find R2(x).
((c)) Use T2(x) to approximate f(1) and f(9).
((d)) Find a theoretical upper bound on the absolute error of each of the approximations in part (c).
((e)) Find a theoretical lower bound on the absolute error of each of the approximations in part (c).
((f)) Find the actual absolute error for each of the approximations in part (c). Verify that they are indeed between the theoretical bounds.
((g)) Sketch graphs of f(x) and T2(x) on the same set of axes for x∈[1,9].