(a) If g(x) = (sin²x)/x², use a calculator or computer to make a table of approximate values of ∫^t₁ g(x) dx for t = 2, 5, 10, 100, 1000, and 10,000. Does it appear that ∫^∞₁ g(x) dx is convergent?

(b) Use the Comparison Theorem with f(x) = 1/x² to show that ∫^∞₁ g(x) dx is convergent.

(c) Illustrate part (b) by graphing f and g on the same screen for 1 ≤ x ≤ 10. Use your graph to explain intuitively why ∫^∞₁ g(x) dx is convergent.