Let $\mathbf { F } ( x , y , z ) = x y i$

question 52

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = x y i$ and let S be the boundary surface of the solid $E = \{ ( x , y , z ) \mid 0 \leq x \leq 1,0 \leq y \leq 1,0 \leq z \leq 1 \}$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

• A) \(0\)
• B) \(\frac { 1 } { 4 }\)
• C) \(\frac { 1 } { 3 }\)
• D)
• \(\frac { 1 } { 2 }\)
• E) \(\frac { 2 } { 3 }\)
• F)
• \(\frac { 3 } { 4 }\)
• G)
• \(1\)
• H) \(\frac { 3 } { 2 }\)

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Definitions:

Differentiated Products

Goods or services that are distinct in quality, features, or branding, which are not perfect substitutes and allow for product variety in the market.

Control Over Price

Regulatory or market-driven mechanisms that influence the setting and adjustment of prices for goods and services.

Monopolistically Competitive Industry

A market structure characterized by many firms selling products that are similar but not identical, allowing for competition based on factors other than price.

Product Differentiation

The strategy businesses use to distinguish their products from those of competitors, through variations in quality, features, design, or branding.