Let {rl, r2, . . . , rn . . .} be an enumeration of the rational numbers in I := [0, 1], and let In :I -+ JRbe definedto be 1 if x = rl, .. " rn and equal to 0 otherwise. Show that In is Riemannintegrable for each n E N, that II (x) ::s 12 (x) ::s .. . ::s In (x) ::s .. . and that I (x) := lim(ln (xis the Dirichlet function, which is not Riemann integrable on [0, 1].

Chapter 15 — Applications of Aqueous Equilibria 1 I. Acid / Base Titration Calculations: A. strong acid with strong base, pH at equivalence point = 7 B. strong acid with weak base, pH at equivalence point < 7 weak acid with strong base, pH at equivalence point > 7 C. D. weak acid with weak base, pH at equivalence point that depends on K , Ka b...