Solve the Problem $$\iiint \left( 1 - \frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 64 } - \frac { z ^ { 2 } } { 64 } \right) d V ?$$

question 221

Multiple Choice

Solve the problem.
-What domain D in space minimizes the value of the integral
$$\iiint \left( 1 - \frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 64 } - \frac { z ^ { 2 } } { 64 } \right) d V ?$$

• A) \(\mathrm { D } =\) the boundary and interior of the sphere \(x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 64\).
• B) \(D =\) the boundary of the sphere \(x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 64\).
• C) \(\mathrm { D } = 23\)
• D) No such maximum domain exists.

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Definitions:

Psychobabble

The use of jargon from psychology and psychotherapy in a manner that is understood to be pretentious or meaningless.

Empirical Evidence

Information obtained through observation, experimentation, or experience, as opposed to theory or belief, used as the basis for knowledge.

Choice Overload

The phenomenon where having too many options can lead to difficulty in making decisions and potential dissatisfaction with the chosen option.

Rumination

The repetitive, often compulsive, focus on the symptoms of one's distress, and its possible causes and consequences, rather than on solutions.