Let P(n) be the perimeter of an n gon inscribed in a unit circle (Figure 7) (a) Explain, intuitively, why P(n) approaches 2 as n (b) Show that P(n) 2n sin () (c) Combine (a) and (b) to conclude that (d) Use this to give another argument that limsin () 1 11 00...

a As n the ngon approaches a circle of radius 1 Therefore the perimeter of the ngon approaches the c ...

Let P(n) be the perimeter of an n-gon inscribed in a unit circle (Figure 7). (a) Explain,

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Let P(n) be the perimeter of an n-gon inscribed in a unit circle (Figure 7).
(a) Explain, intuitively, why P(n) approaches 2π as n→ ∞.
(b) Show that P(n) = 2n sin (π).

(d) Use this to give another argument that sin 0 lim 0-0 0 = 1.

ooo n=9 n=6 n = 12

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Let P(n) be the perimeter of an n-gon inscribed in a unit circle (Figure 7). (a) Explain,

Question:

limsin () = 1. 11-00

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a As n the ngon approaches a circle of radius 1 Therefore the perimeter of the ngon approaches the c...View the full answer

Calculus

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