The Trumpet Surface, S, Is Given Parametrically By $$\vec { r } ( s , t ) = s \vec { 2 } \cos t \vec { i } + s \vec { j } + s ^ { 2 } \sin t k , 0 £ s £ 5,0 £ t £ 2 \pi$$

question 22

Essay

The trumpet surface, S, is given parametrically by $$\vec { r } ( s , t ) = s \vec { 2 } \cos t \vec { i } + s \vec { j } + s ^ { 2 } \sin t k , 0 £ s £ 5,0 £ t £ 2 \pi$$ If S has outward pointing normal, use an appropriate line integral to calculate $\hat { Q } { \operatorname { curl } } ( z \vec { i } + \cos ( x + z ) \vec { j } - x \vec { k } ) \times \vec { d A }$

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Definitions:

Substitution

The economic principle describing how consumers or producers switch between goods or resources as relative prices or availability change.

Quart

A unit of liquid volume equal to two pints, approximately 0.946 liters in the United States.

Pound

A unit of currency used in the United Kingdom and other areas, or a unit of weight equal to 16 ounces.

Convex Preferences

Consumer preferences that signify a desire for diversified bundles of goods, represented by convex-shaped indifference curves.