Vector valued function

JJ007

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Nov 7, 2009
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Find the domain of the vector valued functions
r(t)=3ti1t2j+4k\displaystyle r(t)=3ti- \sqrt{1-t^2}j+4k
\(\displaystyle $-1\leq$ t $\leq$1?\)

r(t)=1ti+ln(t)j+t2k\displaystyle r(t)=\frac{1}{t}i+ln(-t)j+t^2k
(,o)?\displaystyle (-\infty,o)?

Thanks
 
JJ007 said:
Find the domain of the vector valued functions
\(\displaystyle r(t)=3ti- sqrt{1-t^}j+4k\)

I think you are missing a set of parenthesis. Is your function:

r(t)=3ti - sqrt(1-t^)j + 4k <<< What's the intention of the carret sign over 't'?


\(\displaystyle $-1\leq$ t $\leq$1?\)

r(t)=1ti+ln(t)j+t2k\displaystyle r(t)=\frac{1}{t}i+ln(-t)j+t^2k
(,o)?\displaystyle (-\infty,o)?

Thanks
 
Subhotosh Khan said:
JJ007 said:
Find the domain of the vector valued functions
\(\displaystyle r(t)=3ti- sqrt{1-t^}j+4k\)

I think you are missing a set of parenthesis. Is your function:

r(t)=3ti(1t2)j+4k\displaystyle r(t)=3ti - \sqrt{(1-t^2)}j + 4k <<< What's the intention of the carret sign over 't'?


\(\displaystyle $-1\leq$ t $\leq$1?\)

r(t)=1ti+ln(t)j+t2k\displaystyle r(t)=\frac{1}{t}i+ln(-t)j+t^2k
(,o)?\displaystyle (-\infty,o)?

Thanks
Sorry, fixed it
 
Now, unless stated otherwise, we consider the domain of the vectorvalued function\displaystyle Now, \ unless \ stated \ otherwise, \ we \ consider \ the \ domain \ of \ the \ vector-valued \ function

r to be the intersection of the domain of the component functions f, g, and h.\displaystyle r \ to \ be \ the \ intersection \ of \ the \ domain \ of \ the \ component \ functions \ f, \ g, \ and \ h.

Hence, r(t) = 3ti1t2j+4k.\displaystyle Hence, \ r(t) \ = \ 3ti-\sqrt{1-t^2}j+4k.

f(t) = 3t, domain = all reals.\displaystyle f(t) \ = \ 3t, \ domain \ = \ all \ reals.

g(t) = 1t2, domain = [1,1].\displaystyle g(t) \ = \ -\sqrt{1-t^2}, \ domain \ = \ [-1,1].

h(t) = 4, domain = all reals.\displaystyle h(t) \ = \ 4, \ domain \ = \ all \ reals.

Therefore, the domain of r(t) = [1,1].\displaystyle Therefore, \ the \ domain \ of \ r(t) \ = \ [-1,1].

What is the range of r(t)?\displaystyle What \ is \ the \ range \ of \ r(t)?
 
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