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Determine Whether F(x,y,z)=x2cos(x3),yey2,zsinz\mathrm { F } ( x , y , z ) = \left\langle x ^ { 2 } \cos \left( x ^ { 3 } \right) , y e ^ { y ^ { 2 } } , z \sin z \right\rangle

question 14

Essay

Determine whether F(x,y,z)=x2cos(x3),yey2,zsinz\mathrm { F } ( x , y , z ) = \left\langle x ^ { 2 } \cos \left( x ^ { 3 } \right) , y e ^ { y ^ { 2 } } , z \sin z \right\rangle is conservative and if so, find a potential function.


Definitions:

Collectivism

The principle of giving a group priority over each individual in it.

Group Identification

The psychological process by which an individual aligns themselves with the norms, values, and beliefs of a particular group.

Respect For The Elderly

The practice of showing honor and consideration to older individuals, recognizing their contributions and wisdom.

Individualism

A thought school in societal studies that places the freedom of the individual as paramount, in contrast to control by the collective or state.

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