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If we take the central difference twice we get $$\frac{f(x+2h)+f(x-2h)-2f(x)}{4h^2}$$

It is said that taking the forward difference and then the central difference is equal, but I do not get the same expression

$$\frac{f(x+2h)-f(x+h)-f(x)-f(x-h)}{4h^2}$$

newhere
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  • They are equal in the limit of $h \rightarrow 0$ if $f \in C^2$, but are definitely not equal for finite values of $h$. Where does this phrase come from? – lisyarus Aug 28 '19 at 15:31
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    Duplicate of https://math.stackexchange.com/q/123206 – Jean Marie Aug 28 '19 at 15:54

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