If ${ \vec { F } } = 5 y e ^ { x ^ { 2 } }{\vec { i } } + 4 x y e ^ { y} \vec { j } + 4 z \cos ( x y ) \vec { k }$

question 11

Multiple Choice

If ${ \vec { F } } = 5 y e ^ { x ^ { 2 } }{\vec { i } } + 4 x y e ^ { y} \vec { j } + 4 z \cos ( x y ) \vec { k }$ find $\operatorname { div } \vec { F} .$

• A) \(10 x y e ^ { x ^ { 2 } } \vec { i } + \left( 4 x e ^ { y } + 4 x y e ^ { y } \right) \vec { j } + 4 \cos ( x y ) \vec { k }\)
• B) \(10 x y e ^ { x ^ { 2 } } + 4 x e ^ { y } + 4 x y e ^ { y } - 4 \cos ( x y )\)
• C) \(10 x y e ^ { x ^ { 2 } } + 4 x y e ^ { y } + 4 \cos ( x y )\)
• D) \(10 x y e ^ { x ^ { 2 } } + 4 x e ^ { y } + 4 x y e ^ { y } + 4 \cos ( x y )\)
• E) \(5 x y e ^ { x ^ { 2 } } \vec { i } + \left( 4 x e ^ { y } + 4 x y e ^ { y } \right) \vec { j } + 4 \cos ( x y ) \vec { k }\)

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Definitions:

Night Shifts

Work schedules that require employees to work during the night hours, often linked to various health and social concerns.

Performance Level

A measure of the efficacy, efficiency, or quality of an individual's or organization's work output.

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A cognitive bias that leads individuals to attribute their successes to internal factors while blaming external factors for their failures.

Personal Failures

Instances where an individual fails to meet their own standards or expectations, impacting their perception of self-worth or ability to succeed.