ABSTRACT
This equation certainly makes no sense in the general case of a function f: nn ~ nm, but can be reformulated in a way that does. If A: R ~ R is the linear transformation defined by A(h) = f'(a) · h, then equation (l) is equivalent to
( ) 1. f(a + h) - f(a) - A(h) _ 2 _1m h - 0. 11--+0
Equation (2) is often interpreted as saying that A + f(a) is a good approximation to fat a (see Problem 2-9). Henceforth we focus our attention on the linear transformation A and reformulate the definition of differentiability as follows.
