II.
(C) Using separation of variables:
Given initial point (0,0), we have 0 = tan(0 + C); hence C = 0 and the
particular solution is y = tan(x). Because this function has vertical
asymptotes at and the particular solution must be differentiable in
an interval containing the initial point x = 0, the domain is
(C)
(B) From the Riemann Sum, we see then Notice that the
term involving k in the Riemann Sum is not equal to Thus, the
only choice for xk is so a = 0 and so b = 1. Since xk
replaces x, giving the integral
(A) I. converges by the Ratio Test:
diverges by the nth Term Test:
