(a) If a function f is Riemann integrable on [a, b] and |f(x)| ≤ M for some constant M > 0 and for all x ∈ [a, b], show that .
(b) Consider the function f(x) = sin(1/x) on the interval [a, b] := [0.1, 0.4].
Let P = (0.1, 0.2, 0.25, 0.3, 0.35, 0.4) be a partition of [a, b].
i. Calculate the norm of the partition P.
ii. Calculate the Riemann sum where has tags at the right endpoints of the subintervals.
(c) Is f(x) = sin(1/x) Riemann integrable over the interval [−0.1, 0.1]? Explain.