Sample Problem 2: Determine the absolute error and relative error when approximating the derivative of f(x) = -x² + 5x at x=2 using the approximation formula, f'(x) = f(x+h)-f(x) h with h=0.1 Solution: The approximation formula represents the approximated value while the true value is simply the derivative f'(x) at x=2. AV: f'(x) = f(x + h) − f (x) _ [-(x + 0.1)² +5(x + 0.1)] - [-x² + 5x] h 0.1 f'(x) =L-(2 +0.1)? +5(2 + 0.1)] −{-(2)? +5(2)] 0.1 f'(2) = 6.09 - 6 0.1 = 0.9 TV: f'(x) = -2x+5 f'(2) = -2(2) +5=1 Thus, ε = 10.9 = 0.1 0.1 Er == 0.1

Sample Problem 2: Determine the absolute error and relative error when approximating the derivative of f(x) = -x² + 5x at x=2 using the approximation formula, f'(x) = f(x+h)-f(x) h with h=0.1 Solution: The approximation formula represents the approximated value while the true value is simply the derivative f'(x) at x=2. AV: f'(x) = f(x + h) − f (x) _ [-(x + 0.1)² +5(x + 0.1)] - [-x² + 5x] h 0.1 f'(x) =L-(2 +0.1)? +5(2 + 0.1)] −{-(2)? +5(2)] 0.1 f'(2) = 6.09 - 6 0.1 = 0.9 TV: f'(x) = -2x+5 f'(2) = -2(2) +5=1 Thus, ε = 10.9 = 0.1 0.1 Er == 0.1

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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