Find the domain of vector function $\mathbf { r } = \left\langle \sqrt { 1 - t } , \ln t , e ^ { 2 t } \right\rangle$
A)[0,1]
B)(0,1)
C)(0,1]
D)(0,$\infty$)
E)[0,1)
F)(-1,0]
G)(-$\infty$,1]
H)(-$\infty$,1)

Question

Find the domain of vector function $\mathbf { r } = \left\langle \sqrt { 1 - t } , \ln t , e ^ { 2 t } \right\rangle$ 
A)[0,1]
B)(0,1)
C)(0,1]
D)(0,$\infty$)
E)[0,1)
F)(-1,0]
G)(-$\infty$,1]
H)(-$\infty$,1)

Quizplus · Accepted Answer

The domain of the vector function is determined by the intersection of the domains of its component functions. For $\sqrt{1-t}$, $t \leq 1$. For $\ln t$, $t > 0$. Therefore, the domain is the intersection of $t \leq 1$ and $t > 0$, which is $0 < t \leq 1$.

Find the Domain of Vector Function r=⟨1−t,ln⁡t,e2t⟩\mathbf { r } = \left\langle \sqrt { 1 - t } , \ln t , e ^ { 2 t } \right\rangler=⟨1−t​,lnt,e2t⟩

Find the Domain of Vector Function $\mathbf { r } = \left\langle \sqrt { 1 - t } , \ln t , e ^ { 2 t } \right\rangle$