Category:Definitions/Differentiable Vector-Valued Functions

This category contains definitions related to Differentiable Vector-Valued Functions.
Related results can be found in Category:Differentiable Vector-Valued Functions.

$f$ is differentiable at $x \in \R^n$ if and only if there exists a linear transformation $T: \R^n \to \R^m$ and a mapping $r : U \to \R^m$ such that:

$(1): \quad \map f {x + h} = \map f x + \map T h + \map r h \cdot \norm h$

$(2): \quad \ds \lim_{h \mathop \to 0} \map r h = 0$