Use the order n = 2 Taylor approximations, with error term, expanded (a) about a = 1o, for both f(ro- h), and f(xo - 2h) to derive the following formula. f(z0) – 2f(Io – h)+f(zo - 2h) f"(z0) = In big-Oh notation what is the order of the error for this method in terms (b) of step size h? (c) Use the above formula on the data below with h = 0.15 to compute an approximation to f"(1.65). %3D f(x) 1.35 0.2466 1.45 0.2869 1.50 0.3033 1.55 0.3173 1.65 0.3393

Use the order n = 2 Taylor approximations, with error term, expanded (a) about a = 1o, for both f(ro- h), and f(xo - 2h) to derive the following formula. f(z0) – 2f(Io – h)+f(zo - 2h) f"(z0) = In big-Oh notation what is the order of the error for this method in terms (b) of step size h? (c) Use the above formula on the data below with h = 0.15 to compute an approximation to f"(1.65). %3D f(x) 1.35 0.2466 1.45 0.2869 1.50 0.3033 1.55 0.3173 1.65 0.3393

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

- (a)
about a = 1o, for both f(ro-h), and f(xo-2h) to derive the following formula.
Use the order n = 2 Taylor approximations, with error term, expanded
f(ro) - 2f(xo -h) + f(xo-2h)
f"(zo) =
In big-Oh notation what is the order of the error for this method in terms
(b)
of step size h?
(c)
approximation to f"(1.65).
Use the above formula on the data below with h 0.15 to compute an
f(x)
1.35 0.2466
1.45 0.2869
1.50 0.3033
1.55 0.3173
1.65 0.3393

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