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10) Use Newton's method to derive the ancient and long standing divide and average method for finding square roots by hand. It is also known as the Babylonian method. √ can be approximated by iterating x¡+1 using an initial guess xo. Because √ is the positive solution to the equation x² - r = 0, derive the iterating formula above by simplifying the Newton's method formula using ƒ(x) = x² – r. Note that since r is a constant, d/dx(r) = 0 . - 2 1 +

10) Use Newton's method to derive the ancient and long standing divide and average method for finding square roots by hand. It is also known as the Babylonian method. √ can be approximated by iterating x¡+1 using an initial guess xo. Because √ is the positive solution to the equation x² - r = 0, derive the iterating formula above by simplifying the Newton's method formula using ƒ(x) = x² – r. Note that since r is a constant, d/dx(r) = 0 . - 2 1 +

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 82E
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10) Use Newton's method to derive the ancient and long standing divide and average method for finding square roots by hand. It is also known as the Babylonian method. √ can be approximated by iterating X₁ + 1 = using an initial guess xo. Because √ is the positive solution to the equation x² – ² — r = 0, derive the iterating formula above by simplifying the Newton's method formula using ƒ(x) = x² − -r. Note that since r is a constant, d/dx(r) = 0. 1 x₁ +
Transcribed Image Text:10) Use Newton's method to derive the ancient and long standing divide and average method for finding square roots by hand. It is also known as the Babylonian method. √ can be approximated by iterating X₁ + 1 = using an initial guess xo. Because √ is the positive solution to the equation x² – ² — r = 0, derive the iterating formula above by simplifying the Newton's method formula using ƒ(x) = x² − -r. Note that since r is a constant, d/dx(r) = 0. 1 x₁ +
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