(a) A student derived the following: f"(x) ≈ = f'(x + h) — f'(x - h) 2h 1 [f(x+h)-f(x) 2h h f(x) - f(x - h) -h)] h f(x+h) - 2f(x) + f (x − h) 2h² Is this correct or not? Justify your answer. (b) If the approximate formula in (a) is wrong, find a correct one with the order of error.

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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(a) A student derived the following:
f"(x) ≈
f'(x + h) — f'(x – h)
2h
f(x + h) − f (x)
h
f(x) – f (x – h)]
- -
h
2h
f(x + h) − 2ƒ(x) + ƒ (x − h)
2h²
Is this correct or not? Justify your answer.
(b) If the approximate formula in (a) is wrong, find a correct one with the order of error.
Transcribed Image Text:(a) A student derived the following: f"(x) ≈ f'(x + h) — f'(x – h) 2h f(x + h) − f (x) h f(x) – f (x – h)] - - h 2h f(x + h) − 2ƒ(x) + ƒ (x − h) 2h² Is this correct or not? Justify your answer. (b) If the approximate formula in (a) is wrong, find a correct one with the order of error.
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