] [Backwards difference approximation of first derivative] Using Taylor's theorem, in lecture we derived the forward difference ap- oximation to the first derivative. In a similar fashion, derive the backwards fference approximation f(xo)-f(xo-h) 1 = f'(x) = ²h f"(E)

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Chapter2: Second-order Linear Odes
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Taylor's theorem

[3] [Backwards difference approximation of first derivative]
Using Taylor's theorem, in lecture we derived the forward difference ap-
proximation to the first derivative. In a similar fashion, derive the backwards
difference approximation
f(xo) – f(xo - h)
h
assuming that f € C²([a, b]).
= f'(xo) — 1/ h ƒ" (E)
Transcribed Image Text:[3] [Backwards difference approximation of first derivative] Using Taylor's theorem, in lecture we derived the forward difference ap- proximation to the first derivative. In a similar fashion, derive the backwards difference approximation f(xo) – f(xo - h) h assuming that f € C²([a, b]). = f'(xo) — 1/ h ƒ" (E)
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