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.
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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c486e63-3f28-413c-a138-e933f63f2652%2Ffca67921-bb36-4aad-bfe3-57d4b7e19800%2Fygkynro_processed.jpeg&w=3840&q=75)
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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