(a) If g(x) = 1/√x–1, use your calculator or computer to make a table of approximate values of ∫t g(x) dx for t = 5, 10, 100, 1000, and 10,000. Does it appear that is convergent or divergent?
(b) Use the Comparison Theorem with f(x) = 1/√3 to show that is divergent.
(c) Illustrate part (b) by graphing f and on the same screen for 2 < x < 20. Use your graph to explain intuitively why ∫∞ g(x) dx is divergent.