Find the domain of the vector-valued function r(t)=\ln(t-1)i+\t

Pearl Carney 2021-11-21 Answered
Find the domain of the vector-valued function
\(\displaystyle{r}{\left({t}\right)}={\ln{{\left({t}-{1}\right)}}}{i}+\text{Square root}{4}-{t}{j}\)

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Expert Answer

Coon2000
Answered 2021-11-22 Author has 1149 answers
Step 1
This vector valued function is a combination of two functions:
1. Logarithmic function and
2. Square root function
Step 2
For, \(\displaystyle{\ln{{\left({t}-{1}\right)}}}\) to be defined
\(\displaystyle{t}-{1}{>}{0}\Rightarrow{t}{>}{1}\)
For Square root function to be defined
\(\displaystyle{4}-{t}\geq{0}\Rightarrow{t}\le{4}\)
So, the domain is:
\(\displaystyle{\left({1},\ {4}\right]}\)
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