Question

im having trouble with Vector Valued Functions. How do I find the domain of a fn? ex: r(t)=5ti-4tj-(1/t)k

Answer 1

take each component by itself and find the domain of each

Answer 2

t cant be 0

Answer 3

5t can be any real number

Answer 4

-4t can be any real number

however the last

1/t will become undefined at t=0

Answer 5

so the domain has to fit all the components so for what values can all of these components get a value

Answer 6

so its all real numbers not including 0?

Answer 7

the answer would be all real numbers EXCEPT for 0 or

\[(-\infty,0)\cup(0,\infty)\]

Answer 8

awesome! that's what my book says and now i understand why. thank you!