Show that if α and β are Dedekind cuts, then so is α + β = {r1 + r1 : r1 ∈ α and r2 ∈ β}.

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Q: Illustration 25.2: Minimize U= 2x, + 4x, Subject to 4x, + 2x, > 12 3x, + 5x, > 15 5x, + 4x, > 20 X1…

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Q: 8. Determine if the critical point (0,0) of f(x,y) =x³+2xy² – y4 +x² + 3xy+y² +10 is a local…

A: f(x,y) = x3 + 2xy2 - y4 + x2 + 3xy + y2 + 10 =&gt; fx = 3x2 + 2y2 + 2x + 3y      fxx = 6x + 2…

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Q: Write the given system in the form x' = P(t)x+f(t) x' = y+z, y' = z+x, z' = 5y-7

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Q: C 33,5 D= 5, = 35 50 OO

A: c We have to fill in blanks. Here, the first step is given below    3    3,5 5 : 6=5,6 9

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