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.)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.5: Differentials: Linear Approximation
Problem 11E
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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.)
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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