$$\begin{gathered} \mathrm{Give}\mathrm{precise}\mathrm{mathematical}\mathrm{definitions}\mathrm{or}\mathrm{descriptions}\mathrm{of}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{concepts}\mathrm{that}\mathrm{follow}. \\ \mathrm{Then}\mathrm{illustrate}\mathrm{the}\mathrm{definition}\mathrm{with}\mathrm{a}\mathrm{graph}\mathrm{or}\mathrm{an}\mathrm{algebraic}\mathrm{example}. \\ \mathrm{an}\mathrm{arc}\mathrm{length}\mathrm{parametrization}\mathrm{for}\mathrm{the}\mathrm{graph}\mathrm{of}\mathrm{a}\mathrm{differentiable}\mathrm{function}\mathrm{r}\left(\mathrm{t}\right) \end{gathered}$$

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