9. For the following approximation 3f(x) + 4f(x + h) – [(x+ 2h) s'(E) = 2h (a) Take the Taylor series of f(r + h) and f(r+ 2h) for thee first five terms. (b) Prove that the approximation is O(h2). (c) Use the approximation to calculate the derivative of In(3r) at r= 2.0 using h = 0.1. Calculate the relative error.

9. For the following approximation 3f(x) + 4f(x + h) – [(x+ 2h) s'(E) = 2h (a) Take the Taylor series of f(r + h) and f(r+ 2h) for thee first five terms. (b) Prove that the approximation is O(h2). (c) Use the approximation to calculate the derivative of In(3r) at r= 2.0 using h = 0.1. Calculate the relative error.

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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Question

9. For the following approximation
3 (x) + 45(r + h) - S(r + 2h)
s'(r) =
(a) Take the Taylor series of f(r + h) and f(r + 2h) for thee first five terms.
(b) Prove that the approximation is O(h2).
(c) Use the approximation to calculate the derivative of In(3.r) at r = 2.0 using h = 0.1. Calculate the relative error.

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