Determine what is the order of the approximation

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Reference no: EM13283485

Define the operator Dh (where h > 0 ) by
Dh f(x)= [f(x+h) - f(x)]/h
Suppose f has three continues bounded derivatives and letEh f(x) be an approximation to f'(x) where
Eh F = 2 Dh f - D2h f
a) what is the order of this approximation?
b) Suppose |f(x) - g(x)| < = for all x show that anappropriate of h lead to |f'(x)- Eh g(x)| <O = (μ) where μ>0 is as large as possible what is μ?

Reference no: EM13283485

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