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Let f(x) = xe". (a) Apply the composite trapezoid rule with m = 6 to approximate comparing with the correct value. f(x) dr. Compute error by

Let f(x) = xe". (a) Apply the composite trapezoid rule with m = 6 to approximate comparing with the correct value. f(x) dr. Compute error by

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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Let \( f(x) = xe^x \). (a) Apply the composite trapezoid rule with \( m = 6 \) to approximate \(\int_0^1 f(x) \, dx\). Compute error by comparing with the correct value. (b) Replace \( f(x) \) by its 4th order Taylor polynomial to approximate \(\int_0^1 f(x) \, dx\). Compute error by comparing with the correct value. (c) Make a table of error of three-point centered-difference formula for \( f'(0) \) with \( h = 0.1, 0.01, 0.001 \).
Transcribed Image Text:Let \( f(x) = xe^x \). (a) Apply the composite trapezoid rule with \( m = 6 \) to approximate \(\int_0^1 f(x) \, dx\). Compute error by comparing with the correct value. (b) Replace \( f(x) \) by its 4th order Taylor polynomial to approximate \(\int_0^1 f(x) \, dx\). Compute error by comparing with the correct value. (c) Make a table of error of three-point centered-difference formula for \( f'(0) \) with \( h = 0.1, 0.01, 0.001 \).
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