Let f be C3 on some open interval S containing x0. For every x S - x0,

Let f be C3 on some open interval S Š† „œ containing x0. For every x ˆˆ S - x0,

where

That is, the approximation error becomes very small as x †’ 0. In this sense, (18) is the best quadratic approximation to f in a neighborhood of x0.

Transcribed Image Text:

e(x) lim