Let $S$ Be the Cube with Vertices $( \pm 1 , \pm 1 , \pm 1 )$

question 8

Multiple Choice

Let $S$ be the cube with vertices $( \pm 1 , \pm 1 , \pm 1 )$ . Approximate $\iint _ { S } \sqrt { x ^ { 2 } + 2 y ^ { 2 } + 7 z ^ { 2 } }$ by using a
Riemann sum as in Definition 1, taking the patches $S _ { i j }$ to be the squares that are the faces of the cube and the points $P _ { i j }$ to be the centers of the squares.

• A) \(8 ( 3 + \sqrt { 2 } )\)
• B) \(8 ( 3 + \sqrt { 7 } )\)
• C) \(8 ( 1 + \sqrt { 2 } + \sqrt { 7 } )\)
• D) \(4 ( 1 + \sqrt { 2 } + \sqrt { 7 } )\)
• E) none of these

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Definitions:

Meta-analysis

A statistical technique that combines the results of multiple studies to determine the overall effect of a particular intervention or variable.

Complex Trauma

Exposure to multiple traumatic events, often of an invasive and interpersonal nature, leading to wide-ranging, long-term effects.

Mild Neuroses

Less severe forms of neurotic disorders that involve chronic distress but do not impede the ability to function in daily life.

Adjustment Disorders

Emotional or behavioral responses to identifiable stressors, occurring within three months of the stressor and causing significant impairment.