Determine Whether or Not the Vector Field $\mathbf { F } ( x , y , z ) = z \mathbf { i } + 2 y z \mathbf { j } + \left( x + y ^ { 2 } \right) \mathbf { k }$

question 40

Essay

Determine whether or not the vector field $\mathbf { F } ( x , y , z ) = z \mathbf { i } + 2 y z \mathbf { j } + \left( x + y ^ { 2 } \right) \mathbf { k }$ is conservative. If it is conservative, find a function f such that $\mathbf { F } = \nabla f$ .

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Definitions:

Cash Dividends

Payments made by a corporation to its shareholders, usually as a distribution of profits.

Associate

A term that may refer to a business partner, an employee position within a company, or a relationship between entities where one has significant influence over the other.

Equity Method

An accounting technique used by a company to record its investment in another company when it has significant influence but does not have full control over that company.