$$\text { Find the domain of the vector function } \mathbf { r } ( t ) = 8 t \mathbf { i } + \frac { 1 } { t - 3 } \mathbf { j } \text {. }$$ Select the correct answer.
A) $( - \infty , - 8 ) \cup ( - 8 , \infty )$
B) $( - \infty , 3 ) \cup ( 3 , \infty )$
C) $( - \infty , - 3 ) \cup ( - 3 , \infty )$
D) $( - \infty , 8 ) \cup ( 8 , \infty )$

Question

Quizplus · Accepted Answer

The domain of the given vector function is the set of all possible values of $t$ such that $\frac{1}{t-3}$ is defined. Since division by zero is undefined, we have $t-3
eq 0$, which gives $t
eq 3$. Therefore, the domain of $\mathbf{r}(t)$ is $( - \infty , 3 ) \cup ( 3 , \infty )$, which is the answer given in choice B.

Find the domain of the vector function r(t)=8ti+1t−3j. \text { Find the domain of the vector function } \mathbf { r } ( t ) = 8 t \mathbf { i } + \frac { 1 } { t - 3 } \mathbf { j } \text {. } Find the domain of the vector function r(t)=8ti+t−31​j.

$\text { Find the domain of the vector function } \mathbf { r } ( t ) = 8 t \mathbf { i } + \frac { 1 } { t - 3 } \mathbf { j } \text {. }$