Determine Whether or Not $\mathbf { F } ( x , y ) = ( y \cos x - \cos y ) \mathbf { i } + ( \sin x + x \sin y ) \mathbf { j }$

question 32

Essay

Determine whether or not $\mathbf { F } ( x , y ) = ( y \cos x - \cos y ) \mathbf { i } + ( \sin x + x \sin y ) \mathbf { j }$ is a conservative vector field. If it is, find a function f such that $\mathbf { F } = \nabla f$

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Definitions:

Earned Income Tax Credit (EITC)

A refundable tax credit for low- to moderate-income working individuals and families, aimed at reducing the tax burden and encouraging employment.

Utilitarianism

A theory in normative ethics holding that the best action is the one that maximizes utility, generally defined as that which produces the greatest well-being of the greatest number of people.

Liberalism

An ideology that upholds the values of autonomy, approval by those governed, and impartiality in legal matters.

Libertarianism

The political philosophy according to which the government should punish crimes and enforce voluntary agreements but not redistribute income.