Concept explainers
(a)
Domain of the given
Answer to Problem 1CRE
Solution:
Domain of the given vector-valued function is .
Explanation of Solution
Given:
We have been given a vector valued function:
Key concepts used:
Domain of a rational function is all real numbers except when denominator is zero. Domain of inverse sine function is
Calculation:
In order to find the domain of a vector valued function, we find the domains of all the components of the vector function and then we consider the intersection of all the domains.
Domain of the first component is all real numbers except 0. Thus, domain of the first component is .
Domain of the second component is all real numbers except . Thus, domain of the second component is .
Domain of the third component is .
For writing the domain of the entire vector valued function, we consider the intersection of all three domains. Thus, the domain of the given vector valued function is .
Conclusion:
The domain of the given vector valued function has been found by first finding the domains of each of the components and then considering the intersection.
(b)
Domain of the given vector valued function.
Answer to Problem 1CRE
Solution:
Domain of the given vector-valued function is .
Explanation of Solution
Given:
We have been given a vector valued function:
Key concepts used:
Domain of a rational function is all real numbers except when denominator is zero. Domain of inverse sine function is
Calculation:
In order to find the domain of a vector valued function, we find the domains of all the components of the vector function and then we consider the intersection of all the domains.
Domain of the first component is .
Domain of the second component is .
Domain of the third component is .
For writing the domain of the entire vector valued function, we consider the intersection of all three domains. Thus, the domain of the given vector valued function is .
Conclusion:
The domain of the given vector valued function has been found by first finding the domains of each of the components and then considering the intersection.
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Chapter 14 Solutions
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