Using Green's Theorem, Compute the Counterclockwise Circulation of F Around $\mathbf { F } = \sin 5 y \mathbf { i } + \cos 7 x \mathbf { j } ; \mathrm { C }$

question 207

Multiple Choice

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
- $\mathbf { F } = \sin 5 y \mathbf { i } + \cos 7 x \mathbf { j } ; \mathrm { C }$ is the rectangle with vertices at $( 0,0 ) , \left( \frac { \pi } { 7 } , 0 \right) , \left( \frac { \pi } { 7 } , \frac { \pi } { 5 } \right)$ , and $\left( 0 , \frac { \pi } { 5 } \right)$

• A) \(- \frac { 2 } { 5 } \pi\)
• B) \(- \frac { 4 } { 5 } \pi\)
• C) \(\frac { 2 } { 5 } \pi\)
• D) 0

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Definitions:

MC Curve

A graph representing the marginal cost of producing an additional unit of a good or service, usually upward sloping, reflecting increasing costs.

AVC Curve

The graphical representation of the average variable cost per unit of output over various levels of production.

Marginal Cost Curve

A graphical representation showing how the cost of producing one additional unit of a good changes as production volume changes.

Perfect Competition

Perfect competition describes a market structure where many firms sell identical products, no single buyer or seller can influence the market price, and there is free entry and exit of firms.