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The quadratic term in a Taylor series expansion of f can be used to define a more accurate x from x,. This means we define x as the root of the quadratic 0= f(x,) + (x – x,)f'(x,)+(x -x,)S"(x,). This leads to the iteration 2f(x,) f'(x,) ± IS"(x,)]– 2f(x, )S"(x,) where we choose the sign in the denominator to make x, closer to x,, i.e., to maximise X+1 = x, 'n+1 the magnitude of the denominator. Define f(x) = x² - 5. Use EXCEL and apply this method to find an estimation for 5 correct to four decimal places. Start with x, = 2.

The quadratic term in a Taylor series expansion of f can be used to define a more accurate x from x,. This means we define x as the root of the quadratic 0= f(x,) + (x – x,)f'(x,)+(x -x,)S"(x,). This leads to the iteration 2f(x,) f'(x,) ± IS"(x,)]– 2f(x, )S"(x,) where we choose the sign in the denominator to make x, closer to x,, i.e., to maximise X+1 = x, 'n+1 the magnitude of the denominator. Define f(x) = x² - 5. Use EXCEL and apply this method to find an estimation for 5 correct to four decimal places. Start with x, = 2.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 5E
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The quadratic term in a Taylor series expansion of f can be used to define a more accurate x1 from x, . This means we define x as the root of the quadratic 'n+1 0 = f(x,)+(x- x,)f'(x,)+÷(x- 1 -x,)/"(x,). This leads to the iteration 2f(x,) f'(x,)± [S"(x, )]– 2f(x,)f"(x,)' Xp+1 = x, where we choose the sign in the denominator to make x,1 closer to x,, i.e., to maximise n+1 the magnitude of the denominator. Define f(x) = x –-5. Use EXCEL and apply this method to find an estimation for 5 correct to four decimal places. Start with x, = 2.
Transcribed Image Text:The quadratic term in a Taylor series expansion of f can be used to define a more accurate x1 from x, . This means we define x as the root of the quadratic 'n+1 0 = f(x,)+(x- x,)f'(x,)+÷(x- 1 -x,)/"(x,). This leads to the iteration 2f(x,) f'(x,)± [S"(x, )]– 2f(x,)f"(x,)' Xp+1 = x, where we choose the sign in the denominator to make x,1 closer to x,, i.e., to maximise n+1 the magnitude of the denominator. Define f(x) = x –-5. Use EXCEL and apply this method to find an estimation for 5 correct to four decimal places. Start with x, = 2.
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