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Evaluate Sf(x,y,z)dS\iint _ { S } f ( x , y , z ) d S

question 77

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Evaluate Sf(x,y,z) dS\iint _ { S } f ( x , y , z ) d S
f(x,y,z) =z;Sf ( x , y , z ) = z ; S is the part of the torus with vector representation
r(u,v) =(5+3cosv) cosui+(5+3cosv) sinuj+3sinvk,0u2π,0vπ2.\mathbf { r } ( u , v ) = ( 5 + 3 \cos v ) \cos u \mathbf { i } + ( 5 + 3 \cos v ) \sin u \mathbf { j } + 3 \sin v \mathbf { k } , 0 \leq u \leq 2 \pi , 0 \leq v \leq \frac { \pi } { 2 } .

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Definitions:

Substitutes

Goods or services that can be used in place of each other, fulfilling the same needs or desires.

Complements

Goods or services that are used together, where the use or consumption of one enhances the use or consumption of the other.

Law Of Supply

The Law of Supply states that, all else being equal, an increase in price results in an increase in the quantity supplied.

Quantity Supplied

The supply of a good or service that businesses intend to sell, given a certain price point.

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