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

question 6

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:

Indifference Curves

Graphical representations of all the combinations of goods and services that provide equal satisfaction to a consumer.

Income

The monetary return or earnings received by an individual or entity, often measured on a regular basis, such as monthly or annually.

Consumption Bundle

A combination of goods and services that a consumer chooses to consume given their budget constraints.

Utility Function

A mathematical representation of how consumers rank different bundles of goods according to their level of satisfaction or utility.