Solve the Problem $\mathrm { D }$ In Space Maximizes the Value of the Integral

question 34

Multiple Choice

Solve the problem.
-What domain $\mathrm { D }$ in space maximizes the value of the integral
$$\iiint \left( \frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } + \frac { z ^ { 2 } } { 4 } - 1 \right) d V ?$$

• A) \(D =\) the boundary of the ellipsoid \(\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } + \frac { z ^ { 2 } } { 4 } = 1\).
• B) \(D =\) the boundary and interior of the ellipsoid \(\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } + \frac { z ^ { 2 } } { 4 } = 1\).
• C) \(\mathrm { D } = \mathcal { R } ^ { 3 }\)
• D) No such minimum domain exists.

Apply knowledge of strategic moves in conflict and cooperation situations.

Analyze how altering payoffs influences players' strategies and outcomes.

Differentiate between simultaneous and sequential games.

Demonstrate understanding of efficiency and optimality in game outcomes.

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