Find the domain of the vector function vec{r}(t)=leftlangle t^{3}, sqrt{t+3}, sqrt{-1-t}right. Domain: {t mid square leq t leq square}

Question

Find the domain of the vector function vec{r}(t)=leftlangle t^{3}, sqrt{t+3}, sqrt{-1-t}>right. Domain: {t mid square leq t leq square}

Accepted Answer

Step:1 ：The vector function (vec{r}(t)=leftlangle t^{3}, sqrt{t+3}, sqrt{-1-t}rightrangle) is defined only when (t+3geq 0) and (-1-tgeq 0).Step:2 ：From (t+3geq 0), we get (tgeq -3).Step:3 ：From (-1-tgeq 0), we get (tleq -1).Step:4 ：Hence, the domain of (vec{r}(t)) is (boxed{[-3,-1]}).

Answer

Step: 1 ：The vector function (vec{r}(t)=leftlangle t^{3}, sqrt{t+3}, sqrt{-1-t}rightrangle) is defined only when (t+3geq 0) and (-1-tgeq 0).Step: 2 ：From (t+3geq 0), we get (tgeq -3).Step: 3 ：From (-1-tgeq 0), we get (tleq -1).Step: 4 ：Hence, the domain of (vec{r}(t)) is (boxed{[-3,-1]}).

Find the domain of the vector function $\vec{r}(t)=\left\langle t^{3}, \sqrt{t+3}, \sqrt{-1-t}> \right.$ Domain: $\{t \mid \square \leq t \leq \square\}$

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