The quadratic term in a Taylor series expansion of f can be used to define a moreaccurate x from x, . This means we define xas the root of the quadraticn+110 = f(x,) +(x– x,)f"(x,) + -(x- x,)f"(x,).This leads to the iteration2f (x,)f'(x,) ± V[S"(x,)]– 2f(x,)f"(x,)'where we choose the sign in the denominator to make xxe = x,n+1|closer to x„, i.e., to maximisethe magnitude of the denominator.Define f(x) = x² - 5. Use EXCEL and apply this method to find an estimation for 5correct to four decimal places. Start with x, = 2.

To input the formulas in EXCEL, first we need to find the expressions of single and double…

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 'n+1 1 (х- This leads to the iteration 2f(x,) f"(x,) ± VIS"(x,)]–2fS (x, )S"(x,) ' Xp+1 = x, where we choose the sign in the denominator to make xXps1 closer to x,, i.e., to maximise 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 'n+1 1 (х- This leads to the iteration 2f(x,) f"(x,) ± VIS"(x,)]–2fS (x, )S"(x,) ' Xp+1 = x, where we choose the sign in the denominator to make xXps1 closer to x,, i.e., to maximise 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.

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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Question

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
n+1
1
0 = f(x,) +(x– x,)f"(x,) + -(x- x,)f"(x,).
This leads to the iteration
2f (x,)
f'(x,) ± V[S"(x,)]– 2f(x,)f"(x,)'
where we choose the sign in the denominator to make x
xe = x,
n+1
|closer to x„, i.e., to maximise
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.

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