Mathematics-Online lexicon: Tangent

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	Mathematics-Online lexicon:
	Tangent

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The tangent of a differentiable parametrized curve $t\mapsto(f_1(t),\ldots,f_n(t))^{\operatorname t}$ in the point $f\left(t_0\right)$ is the line

$\displaystyle f(t_0) + f^\prime(t_0)(t-t_0)\, , \quad t \in \mathbb{R}$

provided at least one component $f^\prime_i(t_0)$ of the tangent vector is different from zero.

$\includegraphics[width=0.55\linewidth]{a_tangente}$

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Examples:

automatically generated 5/30/2011