Using the Divergence Theorem, Find the Outward Flux of F $\mathbf { F } = 3 x y ^ { 2 } i + 3 x ^ { 2 } y j + 6 x y \mathbf { k } ;$

question 13

Multiple Choice

Using the Divergence Theorem, find the outward flux of F across the boundary of the region D.
- $\mathbf { F } = 3 x y ^ { 2 } i + 3 x ^ { 2 } y j + 6 x y \mathbf { k } ;$ D: the region cut from the solid cylinder $x ^ { 2 } + y ^ { 2 } \leq 9$ by the planes $z = 0$ and $z = 6$

• A) \(2916 \pi\)
• B) \(729 \pi\)
• C) \(\frac { 729 } { 2 } \pi\)
• D) \(1458 \pi\)

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Definitions:

Expense Function

A mathematical function that describes the cost associated with a particular level of production or activity.

Revenue Function

A Revenue Function is a mathematical representation of how a company's revenue is dependent on the selling price and quantity of goods or services sold.

Supply Curves

Graphs showing the relationship between the price of a good and the quantity of that good a seller is willing to supply.

Demand Curves

A graphical representation showing the relationship between the price of a good and the quantity demanded by consumers.