146. A recursive definition of ¤/2 If you start with x1 = 1 and define the subsequent terms of {xn} + cos x„-1, you generate a sequence that converges by the rule Xn Xn-1 rapidly to /2. (a) Try it. (b) Use the accompanying figure to explain why the convergence is so rapid. y cos Xn – 1 Xn – 1 Xn - 1

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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146. A recursive definition of ¤/2 If you start with x1 = 1 and
define the subsequent terms
of {xn}
+ cos x„-1, you generate a sequence that converges
by the rule
Xn
Xn-1
rapidly to /2. (a) Try it. (b) Use the accompanying figure to
explain why the convergence is so rapid.
y
cos Xn – 1
Xn – 1
Xn - 1
Transcribed Image Text:146. A recursive definition of ¤/2 If you start with x1 = 1 and define the subsequent terms of {xn} + cos x„-1, you generate a sequence that converges by the rule Xn Xn-1 rapidly to /2. (a) Try it. (b) Use the accompanying figure to explain why the convergence is so rapid. y cos Xn – 1 Xn – 1 Xn - 1
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