Consider the functions where n is a positive integer. a. Show that these functions are even. b.

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Consider the functions F(x) .2n r2n + 1 where n is a positive integer.

a. Show that these functions are even.

b. Show that the graphs of these functions intersect at the points (±1, 1/2), for all positive values of n.

c. Show that the inflection points of these functions occur at 2n 2n х — + V 2n + 1 for all positive values of n.

d. Use a graphing utility to verify your conclusions.

e. Describe how the inflection points and the shape of the graphs change as n increases.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

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