Let x1 = 2 and let xn+1 = 1/2 *xn + 1/xn. a. Prove that xn is decreasing and bounded from below. Hint: First prove that x^2 n+1 − 2 > 0. b. Determine limn→∞xn.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

Let x1 = 2 and let xn+1 = 1/2 *xn + 1/xn.

a. Prove that xn is decreasing and bounded from below. Hint: First prove that x^2 n+1 − 2 > 0.

b. Determine limn→∞xn.

x+1-2 > 0.
Transcribed Image Text:x+1-2 > 0.
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