Consider a smooth function f such that f'(0) = -2. Given the following approximations of order 2 of f'(0): -2.040608 with h=0.1 and -2.010038 with h=0.05. Applying an extrapolation process, the improved approximation of f'(0) is 0.249999 This option None of the answers -1.999849 This option -0.499998
Consider a smooth function f such that f'(0) = -2. Given the following approximations of order 2 of f'(0): -2.040608 with h=0.1 and -2.010038 with h=0.05. Applying an extrapolation process, the improved approximation of f'(0) is 0.249999 This option None of the answers -1.999849 This option -0.499998
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
![Consider a smooth function f such that f'(0) =-2. Given the following approximations
of order 2 of f'(0): -2.040608 with h 0.1 and-2.010038 with h=0.05.
Applying an extrapolation process, the improved approximation of f'(0) is
0.249999
-1.999849
This option
This option
None of the answers
-0.499998](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feebad5d2-9558-4c57-bf2b-c1d0cdeb52ad%2F4d590969-03c8-4a5f-bb3b-9fb52fdbecba%2Ft3arykq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a smooth function f such that f'(0) =-2. Given the following approximations
of order 2 of f'(0): -2.040608 with h 0.1 and-2.010038 with h=0.05.
Applying an extrapolation process, the improved approximation of f'(0) is
0.249999
-1.999849
This option
This option
None of the answers
-0.499998
![Gmail
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O Maps Cubic spline interp.
* numerical defferent.
aMas comp Simpson's Ru..
a comp Trapezoidal R..
Derivative Calculato..
Question
Suppose f"(x) = N,(h) + a,h² + azh* + azh6 + …
Using Richardson's extrapolation which of the following is true:
N,(h) =
with error of order 0(h)
N(h) =
with error of order O(h)
15
This option
O This option
None of the answers
N() =
with error of onder O)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feebad5d2-9558-4c57-bf2b-c1d0cdeb52ad%2F4d590969-03c8-4a5f-bb3b-9fb52fdbecba%2Fj548sts_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Gmail
YouTube
O Maps Cubic spline interp.
* numerical defferent.
aMas comp Simpson's Ru..
a comp Trapezoidal R..
Derivative Calculato..
Question
Suppose f"(x) = N,(h) + a,h² + azh* + azh6 + …
Using Richardson's extrapolation which of the following is true:
N,(h) =
with error of order 0(h)
N(h) =
with error of order O(h)
15
This option
O This option
None of the answers
N() =
with error of onder O)
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