(b) Use Taylor's theorem to find the first-order Taylor series for tan a about x = 1 /4 and the asso- ciated remainder term. Hence determine whether the integral TT / 4 dxx o 1 - tan x is convergent or divergent. (c) Show that the integral sin (et ) at OO is convergent. [Hint: Start by making a substitution.] (d) Let [x] denote the greatest integer less than or equal to x. Evaluate the Riemann-Stieltjes integral x da [ac].(b) In this situation, Taylor's theorem states that f(x) = f (7) + (x - 1)f (7) + 2(x - 1)?f"(d) for some x