12.6-bo'lim: Vektor funktsiyalari

1 va 2-masalalar uchun berilgan vektor funksiyaning sohasini toping.

1. \(\displaystyle \vec r\left( t \right) = \left\langle {{t^2} + 1,\frac{1}{{t + 2}},\sqrt {t + 4} } \right\rangle \) Yechim
2. \(\vec r\left( t \right) = \left\langle {\ln \left( {4 - {t^2}} \right),\sqrt {t + 1} } \right\rangle \) Yechim

3 – 5 masalalar uchun berilgan vektor funksiyaning grafigini chizing.

1. \(\vec r\left( t \right) = \left\langle {4t,10 - 2t} \right\rangle \) Yechim
2. \(\displaystyle \vec r\left( t \right) = \left\langle {t + 1,\frac{1}{4}{t^2} + 3} \right\rangle \) Yechim
3. \(\vec r\left( t \right) = \left\langle {4\sin \left( t \right),8\cos \left( t \right)} \right\rangle \) Yechim

6 va 7-masalalar uchun vektor funksiyaning grafigini chizmasdan aniqlang.

1. \(\vec r\left( t \right) = \left\langle {3\cos \left( {6t} \right), - 4,\sin \left( {6t} \right)} \right\rangle \) Yechim
2. \(\vec r\left( t \right) = \left\langle {2 - t,4 + 7t, - 1 - 3t} \right\rangle \) Yechim

8 va 9-masalalar uchun ikkita nuqta orasidagi chiziq segmentining tenglamasini yozing.

1. \(\left( {1,3} \right)\) da boshlanib \(\left( { - 4,6} \right)\) da tugaydigan chiziq segmenti. Yechim
2. \(\left( {0,2, - 1} \right)\) da boshlanib \(\left( {7, - 9,2} \right)\) da tugaydigan chiziq segmenti. Yechim