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:

Determinant

A factor or variable that causes a change in an economic model or equation, influencing outcomes like price or quantity.

Frank Knight

An economist known for differentiating between risk (measurable uncertainty) and uncertainty (unmeasurable risk), significantly contributing to the field of economics.

Joseph Schumpeter

An Austrian political economist known for his theories on business cycles, economic development, and the concept of creative destruction.

Profit

The difference between total revenue and total cost.