- #1
Cyn
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1. I have to show that
S1 = {x ∈ R2 : x1 ≥ 0,x2 ≥ 0,x1 + x2 = 2}
is a bounded set.2. So I have to show that sqrt(x1^2+x2^2)<M for all (x1,x2) in S1.3. I have said that M>0 and we have 0<=x1<=2 and 0<=x2<=2.
And x2 = 2-x1
We can fill in sqrt(x1^2 + (2-x1)^2) = sqrt (0^2 + (2-0)^2) = 2 < M = 3.
And we can fill in sqrt (x1^2 + (2-x1)^2) = sqrt (2^2 + (2-2)^2) = 2 < M = 3.
Every value between the 0 and the 2 that satisfy x1+x2 = 2 is smaller than this M. So the set is bounded.
Is this correct?
S1 = {x ∈ R2 : x1 ≥ 0,x2 ≥ 0,x1 + x2 = 2}
is a bounded set.2. So I have to show that sqrt(x1^2+x2^2)<M for all (x1,x2) in S1.3. I have said that M>0 and we have 0<=x1<=2 and 0<=x2<=2.
And x2 = 2-x1
We can fill in sqrt(x1^2 + (2-x1)^2) = sqrt (0^2 + (2-0)^2) = 2 < M = 3.
And we can fill in sqrt (x1^2 + (2-x1)^2) = sqrt (2^2 + (2-2)^2) = 2 < M = 3.
Every value between the 0 and the 2 that satisfy x1+x2 = 2 is smaller than this M. So the set is bounded.
Is this correct?