10.7#1

I am having a bit of an issue with problem 1 on the 10.7 WebWork homework. I believe that WebWork is not grading my work correctly (it is marking a correct answer as incorrect).  The problem is to find the domain of the vector function r(t)=<e^(-4t),t/sqrt(t^2-49),t^(1/3)>.

I calculated the domain of the first component as (-INF,INF).

I calculated the domain of the second component as (-INF,7) U (7,INF).

I calculated the domain of the third component as [0,INF).

Therefore, all of the components should be defined only on the interval (7,INF). I have used Wolfram|Alpha to back me up on this:

However, WebWork marks this answer as incorrect:

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No, it's grading you correctly (this time, although it does make mistakes sometimes).   It's interesting that Wolfram alpha is incorrect, isn't it?So, you made a combination of two mistakes: the domain of the second component is
(-INF,-7) U (7,INF) and the domain of the third component is (-INF,INF)--the cube of a negative number is negative, so likewise for the cube root.  Hence the domain is (-INF,-7) U (7,INF) .