43. Let P(n) be the perimeter of an n-gon inscribed in a unit circle (Figure 8). (a) Explain, intuitively, why P(n) approaches 27 as n → o. (b) Show that P(n) = 2n sin (). (c) Combine (a) and (b) to conclude that lim sin () = 1. sin e 1. (d) Use this to give another argument that lim %3D DOO n= 9 n= 6 n= 12 FIGURE 8
43. Let P(n) be the perimeter of an n-gon inscribed in a unit circle (Figure 8). (a) Explain, intuitively, why P(n) approaches 27 as n → o. (b) Show that P(n) = 2n sin (). (c) Combine (a) and (b) to conclude that lim sin () = 1. sin e 1. (d) Use this to give another argument that lim %3D DOO n= 9 n= 6 n= 12 FIGURE 8
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![43.
Let P(n) be the perimeter of an n-gon inscribed in a unit circle (Figure 8).
(a) Explain, intuitively, why P(n) approaches 27 as n → o.
(b) Show that P(n) = 2n sin ().
(c) Combine (a) and (b) to conclude that lim sin () = 1.
sin e
1.
(d) Use this to give another argument that lim
%3D
DOO
n= 9
n= 6
n= 12
FIGURE 8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01338323-6230-4c23-bd68-d8095f9f6cd8%2Ff652d6fd-f894-4002-95d4-4657869133f1%2F5xp0f1.jpeg&w=3840&q=75)
Transcribed Image Text:43.
Let P(n) be the perimeter of an n-gon inscribed in a unit circle (Figure 8).
(a) Explain, intuitively, why P(n) approaches 27 as n → o.
(b) Show that P(n) = 2n sin ().
(c) Combine (a) and (b) to conclude that lim sin () = 1.
sin e
1.
(d) Use this to give another argument that lim
%3D
DOO
n= 9
n= 6
n= 12
FIGURE 8
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