Asosiy tarkibga o'tish

12.7-bo'lim : Vektor funktsiyalari bilan hisoblash

6. Quyidagi limitning hosilasini hisoblang.

\[\vec r\left( t \right) = \left\langle {\frac{{t + 1}}{{t - 1}},\tan \left( {4t} \right),{{\sin }^2}\left( t \right)} \right\rangle \]
Yechim

Haqiqatan ham bu muammo bilan bu erda ko'p narsa qilish mumkin emas. Biz qilishimiz kerak bo'lgan narsa vektorning barcha komponentlarining hosilasini olishdir.

\[\begin{align*}\vec r'\left( t \right) & = \left\langle {\frac{{\left( 1 \right)\left( {t - 1} \right) - \left( {t + 1} \right)\left( 1 \right)}}{{{{\left( {t - 1} \right)}^2}}},4se{c^2}\left( {4t} \right),2\sin \left( t \right)\cos \left( t \right)} \right\rangle \\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{\left\langle {\frac{{ - 2}}{{{{\left( {t - 1} \right)}^2}}},4se{c^2}\left( {4t} \right),2\sin \left( t \right)\cos \left( t \right)} \right\rangle }}\end{align*}\]

Bo'lim qoidasi (birinchi atama) va zanjir qoidasi (uchinchi atama) kabi asosiy farqlash formulalarini esdan chiqarmaganingizga ishonch hosil qiling.