Find the domain of the vector function rt ln t 1 tsquarero

Find the domain of the vector function. r(t) = (ln (t + 1), t/squareroot 9 - t^2, 2^t) r(t) = cos ti + ln tj + 1/1 - 2 k

Solution

To find the domain,

cos t >= 0

ln t >= 0

1/(t-2) >=0

On solving 1/(t-2) >=0

t-2 <= 0

t <=2

For ln t >=0,

t >=1

So, common part is 1<=t <=2