Consider the functions f(x) = a sin 2x and g(x) = (sin x)/a, where a > 0

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Consider the functions f(x) = a sin 2x and g(x) = (sin x)/a, where a > 0 is a real number.

a. Graph the two functions on the interval [0, π/2], for a = 1/2, 1, and 2.

b. Show that the curves have an intersection point x* (other than x = 0) on [0, π/2] that satisfies cos x* = 1/(2a2), provided a > 1/√2.

c. Find the area of the region between the two curves on [0, x*] when a = 1.

d. Show that as a →1/√2+. The area of the region between the two curves on [0, x*] approaches zero.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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