Category:Differentiable Vector-Valued Functions
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This category contains results about Differentiable Vector-Valued Functions.
Definitions specific to this category can be found in Definitions/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:
- $(1): \quad \map f {x + h} = \map f x + \map T h + \map r h \cdot \norm h$
- $(2): \quad \ds \lim_{h \mathop \to 0} \map r h = 0$
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