?Differentiation of Vector-Valued Functions In Exercises 1-6, find r’(t), \(\mathrm{r}\left(t_{0}\right)\), and \(\mathrm{r’}\left(t_{0}\right)\) for t
Chapter 12, Problem 4(choose chapter or problem)
Differentiation of Vector-Valued Functions In Exercises 1-6, find r’(t), \(\mathrm{r}\left(t_{0}\right)\), and \(\mathrm{r’}\left(t_{0}\right)\) for the given value of \(t_{0}\). Then sketch the plane curve represented by the vector-valued function, and sketch the vectors \(\mathrm{r}\left(t_{0}\right)\), and \(\mathrm{r’}\left(t_{0}\right)\). Position the vectors such that the initial point of \(\mathrm{r}\left(t_{0}\right)\) is at the origin and the initial point of \(\mathrm{r’}\left(t_{0}\right)\) is at the terminal point of \(\mathrm{r}\left(t_{0}\right)\). What is the relationship between \(\mathrm{r’}\left(t_{0}\right)\) and the curve?
\(\mathbf{r}(t)=3 \sin t \mathbf{i}+4 \cos t \mathbf{j}, \quad t_{0}=\frac{\pi}{2}\)
Text Transcription:
r(t_0)
r’(t_0)
r(t)=3 sin ti+4 cos tj, t_0=pi/2
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