Suppose that f is a positive function such that f' is continuous. (a) How is the graph

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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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Calculus Early Transcendentals

ISBN: 9781337613927

9th Edition

Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin

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Question Posted: Jan 13, 2021 06:06 AM

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Suppose that f is a positive function such that f' is continuous. (a) How is the graph

Question:

lim (fx) sin nx n0 JO

Step by Step Answer:

a Since 1 sin 1 we have f x f x sin x fx and the graph of y f x sin n...View the full answer

Calculus Early Transcendentals

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