Let f, qJ: [a, 00) -+ JR.Abel's Test asserts that if f E 'R.*[a,00) and qJis bounded and
Chapter 10, Problem 17(choose chapter or problem)
Let f, qJ: [a, 00) -+ JR.Abel's Test asserts that if f E 'R.*[a,00) and qJis bounded and monotoneon [a, 00), then fqJ E 'R.*[a,00).(a) Show that Abel's Test does not apply to establish the convergence of Jooo(1/ x) sin x dx bytaking qJ(x) := l/x. However,it does apply if we take cp(x) := 1/.JX and use Exercise 14.(b) Use Abel's Test and Exercise 15 to show the convergenceof Jooo(xl(x + 1 sin(x2) dx.(c) Use Abel's Test and Exercise 1~to show the convergenceof Jooox-3/2(x + 1) sin x dx.(d) Use Abel's Test to obtain the convergenceof Exercise 16(f).
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