Suppose that f is a positive function such that f’ is continuous.
(a) How is the graph of y = f(x) sin nx related to the graph of y = f(x) What happens as n → ∞?
(b) Make a guess as to the value of the limit
based on graphs of the integrand.
(c) Using integration by parts, confirm the guess that you made in part (b). [Use the fact that, since f’ is continuous, there is a constant M such that | f'(x) | ≤ M for 0 ≤ x ≤ 1.]
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