Sample Problem 2:Determine the absolute error and relative error when approximating the derivative of f(x) = -x² + 5x atx=2 using the approximation formula,f'(x) =f(x+h)-f(x)hwith h=0.1Solution: The approximation formula represents the approximated value while the true value is simplythe derivative f'(x) at x=2.AV:f(x + h) = f(x) _ [−(x + 0.1)² + 5(x + 0.1)] - [-x² + 5x]f'(x) =h0.1[-(2+0.1)² + 5(2 + 0.1)] − [−(2)² +5(2)]f'(x) =0.16.096f'(2) == 0.9TV:Thus,0.1f'(x) = -2x+5f'(2) = -2(2) +5=1ε = 10.9|= 0.10.1Ep. = = 0.1

Answered: Image /qna-images/answer/327c2d16-71d3-46cd-b22c-4c797acb2d92.jpg

Answered: Determine the absolute error and…

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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