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\noindent {\bf 21-259} \hfill {\bf Calculus in 3-D \hfill Spring 2003\\


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\centerline{\bf Formula Sheet for Test 1}


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$${\displaystyle \frac{ds}{dt}} = |\vec{r}\ \!'(t)|$$


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$$\kappa = \left| {\displaystyle \frac{d \vec{T}}{ds}} \right|$$


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$$\kappa = {\displaystyle \frac{|\vec{r}\ \!'(t) \times \vec{r}\ \!''(t)|}{|\vec{r}'(t)|^3}}$$


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 If $y = f(x)$, then \hspace*{.75in} $\kappa = {\displaystyle \frac{|f''(x)|}{(1+f'(x)^2)^{3/2}}}$.


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