Use Newton's method to approximate a root of the equation x³ + x + 2 = 0 as follows. Let x₁ = 1 be the initial approximation. The second approximation 2 is and the third approximation 3 is (Although these are approximations of the root, enter exact expressions for each approximation.)
Use Newton's method to approximate a root of the equation x³ + x + 2 = 0 as follows. Let x₁ = 1 be the initial approximation. The second approximation 2 is and the third approximation 3 is (Although these are approximations of the root, enter exact expressions for each approximation.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Use Newton's method to approximate a root of the equation x³ + x + 2 = 0 as follows.
Let x₁ = 1 be the initial approximation.
#1
The second approximation 2 is
and the third approximation 3 is
(Although these are approximations of the root, enter exact expressions for each approximation.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef062cf3-42c6-40dd-b939-e326c66e5648%2Fbb9a33fe-0a27-4592-a8bd-030055eaa0ff%2Fxipqid_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use Newton's method to approximate a root of the equation x³ + x + 2 = 0 as follows.
Let x₁ = 1 be the initial approximation.
#1
The second approximation 2 is
and the third approximation 3 is
(Although these are approximations of the root, enter exact expressions for each approximation.)
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