Let $\mathbf { F } ( x , y , z ) = \left( x ^ { 3 } + y z \right) \mathbf { i } + x ^ { 2 } y \mathbf { j } + x z ^ { 2 } \mathbf { k }$

question 138

Short Answer

Let $\mathbf { F } ( x , y , z ) = \left( x ^ { 3 } + y z \right) \mathbf { i } + x ^ { 2 } y \mathbf { j } + x z ^ { 2 } \mathbf { k }$ and let S be the surface of the solid bounded by the spheres $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ and $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 9$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

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Definitions:

Marginal Cost

The augmentation in total expenditure resulting from the manufacture of one more unit of a product or service.

Price

Price refers to the amount of money expected, required, or given in payment for something, representing the value exchange between buyer and seller in a market.

Kinked Demand

A demand curve that has a distinct bend or "kink" at a certain price level, reflecting different elasticity above and below that price.

Marginal Cost

The increase in cost resulting from the production of an extra unit of a good or service.