Find the actual error when the first derivative of f (x) = e-2x at x = 1 is approximated by the following 3-point formula f(x + h) + f(x) – 2f(x – h) f'(x) & 4h with h = 0.3. 0.0431 0.5544 0.2313 0.0343
Find the actual error when the first derivative of f (x) = e-2x at x = 1 is approximated by the following 3-point formula f(x + h) + f(x) – 2f(x – h) f'(x) & 4h with h = 0.3. 0.0431 0.5544 0.2313 0.0343
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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Please solve this two exercise
Transcribed Image Text:Find the actual error when the first derivative of f (x) = e-2* at x = 1 is approximated by the
following 3-point formula
f(x + h) + f (x) – 2f(x – h)
f'(x) &
4h
with h = 0.3.
0.0431
0.5544
0.2313
0.0343
Transcribed Image Text:Let f (x) =
(x-2)2
Using the centered 3-point formula for 1st derivatives:
f'(0) x 0.251255 using h = 0.1
f'(0) x 0.250313 using h = 0.05
Applying Richardson's extrapolation on the above values, we get a better approximation of
f'(0) which is:
-1.99985
O 0.249999
O -0.499998
O 0.234256
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