Determine Whether $\mathbf { F }$ Is Conservative $f$ Such That $\mathbf { F } = \nabla f$

question 35

Short Answer

Determine whether $\mathbf { F }$ is conservative. If so, find a function $f$ such that $\mathbf { F } = \nabla f$ .
$$\mathbf { F } ( x , y , z ) = 4 x ^ { 3 } y ^ { 2 } z ^ { 3 } \mathbf { i } + 2 x ^ { 4 } y z ^ { 3 } \mathbf { j } + 3 x ^ { 4 } y ^ { 2 } z ^ { 2 } \mathbf { k }$$

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Definitions:

Conjugation

A form of genetic transfer where two bacteria temporarily join together and directly transfer genetic material between them.

Sex Pilus

A thin, tube-like structure used by bacteria to transfer genetic material during a form of reproduction called conjugation.

Transduction

The process by which sensory stimuli are converted into electrical signals in the nervous system.

Heterotrophic

An organism that obtains its energy and carbon by consuming other organisms, unable to produce its own food.