"Find the domain of the vector-valued function r(t)=(4−t)2i+t2j−6t" was answered by students like you

skomminbv

Answered question

2021-11-28

Find the domain of the vector-valued function

r (t) = \sqrt{{(4 - t)}^{2}} i + t^{2} j - 6 t k

Huses1969

Beginner2021-11-29Added 18 answers

Step 1
Given vector-valued function

r (t) = \sqrt{{(4 - t)}^{3}} i + t^{2} j - 6 t k

Step 2
For the domain of given function
Here

{(4 - t)}^{2}

is non negative for every real number

\Rightarrow \sqrt{{(4 - t)}^{2}}

is also non negative for every real number

\Rightarrow \sqrt{{(4 - t)}^{2}}

is defined for every real number
And

t^{2}

and

- 6 t

is polynomial function
The domain of polynomial function is every real number.
So,
Domain of

r (t) = R

or
Domain of

r (t) = (- \infty, \infty)

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