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WZ
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Problem 32 Easy Difficulty

Plot the space curve and its curvature function $\kappa(t)$.
Comment on how the curvature reflects the shape of the
curve.
$$\mathbf{r}(t)=\langle t-\sin t, 1-\cos t, 4 \cos (t / 2)\rangle, \quad 0 \leqslant t \leqslant 8 \pi$$

Answer

$$
\kappa(t)=\frac{\left|\mathbf{r}^{\prime}(t) \times \mathbf{r}^{\prime \prime}(t)\right|}{\left|\mathbf{r}^{\prime}(t)\right|^{3}}
$$

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Video Transcript

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WZ
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