Use Newton's method to approximate a root of the equation x³ + x + 3 = 0 as follows. Let x₁ = -1 be the initial approximation. The second approximation ₂ is and the third approximation x3 is 2014 5 74 X (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 + 3 = 0 as follows.
Let 1 =
-1 be the initial approximation.
The second approximation ₂
5
4
and the third approximation x3 is
(Although these are approximations of the root, enter exact expressions for each approximation.)
X
Transcribed Image Text:Use Newton's method to approximate a root of the equation x³ + x + 3 = 0 as follows. Let 1 = -1 be the initial approximation. The second approximation ₂ 5 4 and the third approximation x3 is (Although these are approximations of the root, enter exact expressions for each approximation.) X
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