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5. (a) (b) (c) Consider the mid-point rule for approximating [ f(x) dx = (b − a) f(ª+b). (a Derive the error term; Derive composite mid-point rule and its error; How small should h be to guarantee that the approximation of fe-² dx by composite mid-point rule is within an error of 10-5? (note that: you may use max{ƒ"(x)} ≤ 2.)

5. (a) (b) (c) Consider the mid-point rule for approximating [ f(x) dx = (b − a) f(ª+b). (a Derive the error term; Derive composite mid-point rule and its error; How small should h be to guarantee that the approximation of fe-² dx by composite mid-point rule is within an error of 10-5? (note that: you may use max{ƒ"(x)} ≤ 2.)

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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5. Consider the mid-point rule for approximating a+b [ f(x) dx ≈ (b − a)ƒ (ª + b). 2 (a) (b) (c) Derive the error term; Derive composite mid-point rule and its error; 2dx by e How small should ʼn be to guarantee that the approximation of composite mid-point rule is within an error of 10-5? (note that: you may use max{f"(x)} ≤ 2.) -x²
Transcribed Image Text:5. Consider the mid-point rule for approximating a+b [ f(x) dx ≈ (b − a)ƒ (ª + b). 2 (a) (b) (c) Derive the error term; Derive composite mid-point rule and its error; 2dx by e How small should ʼn be to guarantee that the approximation of composite mid-point rule is within an error of 10-5? (note that: you may use max{f"(x)} ≤ 2.) -x²
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