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Use Taylor to derive a numerical differentiation formula of the formf (x) = Af(x) +...

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Calculus

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Use Taylor to derive a numerical differentiation formula of the formf (x) = Af(x) + Bf (x-h) + Cf (x-2h) (h>0)that has precision O(h) for f sufficiently regular. What is the required regularity for f?Check the accuracy by numerical experiments, one to show the performance and one toshow the necessity of the specified regularity.

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