Chapter 13 - Vector Functions - 13.2 Derivatives and Integrals of Vector Functions - 13.2 Exercises - Page 900: 7

\(a)\) Graphed below \(b)\) \(\vec{r}'(t)=\langle 4\cos t, -2\sin t\rangle\) \(c)\) Graphed below

\(a)\) Graph \(b)\) \(\vec{r}(t)=\langle 4\sin t, -2\cos t\rangle\), finding derivative we have: \[\vec{r}'(t)=\langle 4\cos t, -2\sin t\rangle\] \(c)\) At \(t=3\pi/4\) we have: \[ \vec{r}(3\pi/4)=\langle 2\sqrt{2}, \sqrt{2}\rangle \] \[ \vec{r}'(3\pi/4)=\langle -2\sqrt{2}, \sqrt{2}\rangle \]