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njiokm
Group Title
how to find the vector valued function forming the boundaries by the closed curve defined by connected points (0,0), (2,1), and (1,4)
 2 years ago
 2 years ago
njiokm Group Title
how to find the vector valued function forming the boundaries by the closed curve defined by connected points (0,0), (2,1), and (1,4)
 2 years ago
 2 years ago

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dape Group TitleBest ResponseYou've already chosen the best response.1
You can define the function piecewise, and just let the vector vary along each of the straight line segments connecting the points.
 2 years ago

dape Group TitleBest ResponseYou've already chosen the best response.1
So for the first segment \[ \vec{f_1}(t)=(2t,t) \]
 2 years ago

njiokm Group TitleBest ResponseYou've already chosen the best response.0
so the second is (t,4t) right?
 2 years ago

dape Group TitleBest ResponseYou've already chosen the best response.1
Not really, at t=1 we are at the point (2,1), so you need to trace the function from there. You think correctly, but you need a term to align the endpoints of the segments. With your definition we would jump from (2,1) to (1,4) instantaneously at t=1.
 2 years ago

dape Group TitleBest ResponseYou've already chosen the best response.1
So you basically want \[ \vec{f_1}(1)=\vec{f_2}(1) \\ \vec{f_2}(2)=\vec{f_3}(2) \\ \vec{f_3}(3)=(0,0) \] If each segment should take 1 tunit to trace.
 2 years ago

dape Group TitleBest ResponseYou've already chosen the best response.1
Then the full function is just \[ \vec{f}(t)= \begin{cases} \vec{f_1}(t) & \text{if } 0≤t≤1 \\ \vec{f_2}(t) & \text{if } 1<t≤2 \\ \vec{f_3}(t) & \text{if } 2<t≤3 \end{cases} \]
 2 years ago

njiokm Group TitleBest ResponseYou've already chosen the best response.0
ar.....sorry dude I don't really get it can u give me a final answer i will figure it out myself
 2 years ago

dape Group TitleBest ResponseYou've already chosen the best response.1
The second function could be \[ \vec{f_2}(t)=(t+3,\,3t2) \] and the third \[ \vec{f_3}(t)=(t+3,\,4t+12)\]
 2 years ago

njiokm Group TitleBest ResponseYou've already chosen the best response.0
thanks i will try to figure it out
 2 years ago

dape Group TitleBest ResponseYou've already chosen the best response.1
Here is a picture I think will help a lot, if you think visually dw:1348317929963:dw
 2 years ago

dape Group TitleBest ResponseYou've already chosen the best response.1
I got the lines equations by finding t in terms of x or y in the parametrizations
 2 years ago
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