Let f(x)-12.2-2x-11 and a(z) = x2 + 12n, where Ir] is the largest integer less than or equal to r...
5. Let f : [a, b] → R be bounded, a : [a, b] → R monotonically increasing, and P a partition of [a, b]. (a) Define upper and lower Riemann-Stieltjes sums of f with respect to P and a. (b) Let P' be the partition obtained from P by inserting one additional point x' into the subinterval (2k-1, xk] of P. Prove that for the lower and upper Riemann- Stieltjes sums of f we have L(P, f, a) <L(P',...