# An error formula for linearization

Question: Can anyone shed some light on this formula? I can't find any information on it.

It has three corollaries that I also need to understand:

• Anyone...........? – Paze Mar 21 '14 at 1:06
• I believe that it's wrong to claim that provided $E(x)$ satisfies $E(x) = f(x) - L(x)$, but actually $E(x) \approx f(x) - L(x)$ (because there are more terms in the taylor's formula beyond the second term, and to get the exact error you'll have to sum all of them) – Peeyush Kushwaha Nov 27 '17 at 17:36

Here is a spot light hint for the error formula: It is simply Taylor's theorem for $k=1$.