Show That $\mathbf { F }$ Is Conservative and Find a Function

question 118

Multiple Choice

Show that $\mathbf { F }$ is conservative and find a function $f$ such that $\mathbf { F } = \nabla f$ , and use this result to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where $C$ is any path from $A \left( x _ { 0 } , y _ { 0 } \right)$ to $B \left( x _ { 1 } , y _ { 1 } \right)$ .
$\mathbf { F } ( x , y ) = \left( 15 x ^ { 2 } y ^ { 2 } - 14 x y ^ { 4 } \right) \mathbf { i } + \left( 10 x ^ { 3 } y - 28 x ^ { 2 } y ^ { 3 } \right) \mathbf { j } ; A ( 1 , - 2 )$ and $B ( 1 , - 1 )$

• A) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = 34\)
• B) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = 90\)
• C) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = - 144\)
• D) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = 118\)

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Definitions:

Process of Socialization

The process through which individuals learn and adapt to the norms, values, behaviors, and social skills necessary to interact within their society.

Socialization

The process by which individuals learn and adopt the norms, customs, values, and behaviors appropriate to their society or specific social group.

Secondary Socialization

Is socialization outside the family after childhood.

Anticipatory Socialization

Involves taking on the norms and behaviors of a role to which we aspire.