From the list below, select all TRUE statements. (But do not select any false statements!) If the terms of a series En= (-1)"b, have strictly alternating signs, but the sequence of the numbers { bn } is not monotone decreasing, then according to the Alternating Series Test this series diverges. According to the Integral Test, if the function f(x) satisfies the three conditions of the test, and if the improper integral / f (x) dx converges, then En=If(n) = fitof(x) dx. The Maclaurin series for f (x) = x3 sin (x) has even degree terms only. The partial fraction decomposition of - x2 (x2+3) has the form Bx+ C x2 (x2 +3) + B x2 +3 if the series _n=] an converges, then lim an = 0. 1 -+0o Jo's $2 d * is an improper integral. O En-In . ($)" is a geometric series with the common ratio / = Every bounded monotone sequence converges. By definition, an infinite series is called convergent if and only if the sequence of its partial sums has a limit. 2x2 -5x+1 x2+1 - is a proper rational function. if lim an = 0, then the series 27=1 an converges. If lim an # 0, then _ an diverges 1 -+0o The point with polar coordinates -5, 2 lies on the positive (upper) half of the y-axis. The interval of convergence of a power series always contains at least one point