Economizing Power Series. Define s4(x) as the fourth-degree polynomial approximation from the power series expansion XXXXXXXXXXApproximate s4(x) further by a quadratic by substituting (3/4)(x − 1) for...

Economizing Power Series. Define s4(x) as the fourth-degree polynomial approximation from the power series expansion (7.6.1). Approximate s4(x) further by a quadratic by substituting (3/4)(x − 1) for (x − 1)3 and (x − 1)2 − 1/8 for (x − 1)4; compare the quadratic approximation that follows from these substitutions to the Chebyshev approximation from Exercise 7.3. (These substitutions arise from the minimum norm property of Tn(x): T3(u) = u3 − (3/4)u and T4(u) = u4 − u2 + 1/8.)