Finding the Domain of a Vector Valued Function
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Finding the Domain of a Vector Valued Function


This is a video on finding the domain. The question states: Find the domain of the vector valued function r(t)=1/(t-3) i – t squared j + root(t+1) k. To find the domain of a vector valued function, we find the domain of each of the three components and then take the intersection. Let’s start out with the domain of the first component 1/(t-3). The issue here is that the denominator can’t be 0 or that t-3 is not equal to 0. We get that t is not equal to 3. For the second component -t squared, there are no issues. Polynomials have domain all real numbers, so that doesn’t restrict the domain. For the third component, the square root of t+1, we have to make sure that the inside is greater than or equal to 0, because the square root can’t be negative. So t+1 is greater than or equal to 0. We get that t is greater than or equal to -1. Now let’s just put this together. The domain is the intersection of all the domains. We have to make sure that t is not 3 AND that t is greater than or equal to 1. We get the domain of the vector valued function is the set of all t such that t is not equal to 3 AND t is greater than or equal to -1. I am done with the problem.

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