Find the Correct Identity, If $f$ Is a Scalar Field $\mathbf { F }$

question 59

Multiple Choice

Find the correct identity, if $f$ is a scalar field, $\mathbf { F }$ and $\mathbf { G }$ are vector fields.

• A) \(\operatorname { div } ( f \mathbf { F } ) = f \operatorname { div } ( \mathbf { F } ) + \mathbf { F } \cdot \nabla f\)
• B) \(\quad \operatorname { curl } ( f \mathbf { F } ) = f \operatorname { div } ( \mathbf { F } ) + \mathbf { F } \cdot \nabla f\)
• C) \(\operatorname { div } ( f \mathbf { F } ) = f \operatorname { curl } ( \mathbf { F } ) + ( \nabla f ) \times \mathbf { F }\)
• D) None of these

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Definitions:

Equilibrium Price

The price at which the quantity of a product demanded by consumers equals the quantity supplied by producers, leading to a balance in the market.

Demand Schedule

A chart indicating the amount of a product or service buyers are prepared and capable of buying at different price levels.

Shortage/Surplus

A state in the marketplace where the demand for a good surpasses its supply, causing a shortage, or where the supply of a product outpaces its demand, resulting in a surplus.

Demand Schedule

A chart detailing the amount of a product that buyers are ready and capable of buying at different price levels.