Let $\mathbf { F } ( x , y , z ) = ( z - 4 y \sin x ) \mathbf { i } + x z \mathbf { j } + y z ^ { 2 } \mathbf { k }$

question 24

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = ( z - 4 y \sin x ) \mathbf { i } + x z \mathbf { j } + y z ^ { 2 } \mathbf { k }$ . Find the value of the divergence of F at the point $( 0,0,1 )$ .

• A) \(- 3\)
• B)\(- 2\)
• C)\(- 1\)
• D)\(0\)
• E)\(1\)
• F)\(2\)
• G) \(3\)

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Definitions:

Optimal Values

The most favorable or efficient values that lead to the best outcome in a given situation or model.

Fabrication Labor Constraint

A limitation in the manufacturing process related to the amount of labor available for fabricating products.

Right-hand Sides

In linear programming, these are the values on the right side of the equation, representing the constraints or limits of the resources.

Left-hand Sides

Refers typically to the left side of equations or inequalities in mathematical expressions or models.