- #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.

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?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?