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Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈ f (x − 2h) — 4f (x − h) + 3f (x) 2h Then, the actual error for the approximation of f'(2) with h = 0.1 is most nearly O 0.00346 O 0.01458 O 0.21475 O None of the choices

Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈ f (x − 2h) — 4f (x − h) + 3f (x) 2h Then, the actual error for the approximation of f'(2) with h = 0.1 is most nearly O 0.00346 O 0.01458 O 0.21475 O None of the choices

Advanced Engineering Mathematics
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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Suppose that the first derivative of f(x) = x² In x is approximated by the following formula ƒ'(x) ≈ ƒ (x − 2h) − 4ƒ (x − h) +3f (x) 2h Then, the actual error for the approximation of f'(2) with h = 0.1 is most nearly O 0.00346 O 0.01458 O 0.21475 O None of the choices
Transcribed Image Text:Suppose that the first derivative of f(x) = x² In x is approximated by the following formula ƒ'(x) ≈ ƒ (x − 2h) − 4ƒ (x − h) +3f (x) 2h Then, the actual error for the approximation of f'(2) with h = 0.1 is most nearly O 0.00346 O 0.01458 O 0.21475 O None of the choices
The degree of precision of the following quadrature formula is: 03 02 O 1 Let f(x)= In x. By using the following formula for first derivative approximation: f'(x) f(x-2h)-4f (x − h) + 3f(x) 2h [*f(x) * - 2f (¹) + 3f (0) + ƒ}) We calculate f' (2) using h = 0.1 and h = 0.05 to deduce that the truncation error of this formula is almost: 3 O None of the choices 02 O 4
Transcribed Image Text:The degree of precision of the following quadrature formula is: 03 02 O 1 Let f(x)= In x. By using the following formula for first derivative approximation: f'(x) f(x-2h)-4f (x − h) + 3f(x) 2h [*f(x) * - 2f (¹) + 3f (0) + ƒ}) We calculate f' (2) using h = 0.1 and h = 0.05 to deduce that the truncation error of this formula is almost: 3 O None of the choices 02 O 4
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