Determine Whether F Is Conservative $\mathbf { F } = \nabla f$

question 42

Multiple Choice

Determine whether F is conservative. If so, find a function f such that $\mathbf { F } = \nabla f$ . $\mathbf { F } ( x , y ) = \left( 6 x ^ { 2 } - 4 x ^ { 3 } y \right) e ^ { - 2 x y } \mathbf { i } - 4 x ^ { 4 } e ^ { - 2 x y } \mathbf { j }$

• A) \(f ( x , y ) = \left( 2 x ^ { 3 } - 2 y \right) e ^ { - 2 x y } + C\)
• B) not conservative
• C) \(f ( x , y ) = 2 x ^ { 3 } e ^ { - 2 x y } + C\)
• D) \(f ( x , y ) = \left( 12 - 4 x ^ { 3 } \right) e ^ { - 2 x y } + C\)

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Definitions:

Summary Statistics

Numerical values calculated from a dataset, intended to provide information about the characteristics of the data.

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Quantitative indicators or metrics used to assess, compare, or track performance or progress.

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A group of athletes who compete in track and field events, including running races, jumping, and throwing disciplines.

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Standard Deviation is a measure of the amount of variation or dispersion of a set of values.