Determine Whether or Not Vector Field Is Conservative $f$ Such That $\mathbf { F } = \nabla f$

question 11

Short Answer

Determine whether or not vector field is conservative. If it is conservative, find a function $f$ such that $\mathbf { F } = \nabla f$ .
$$\mathbf { F } ( x , y , z ) = 25 y z e ^ { 5 x x _ { i } } \mathbf { i } + 5 e ^ { 5 x x _ { j } } \mathbf { j } + 25 x y e ^ { 5 x z } \mathbf { k }$$

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Definitions:

Healthy Personality Development

Healthy personality development involves the growth and maturation of an individual's personality traits in a way that fosters well-being and effective coping skills.

Neo-Freudians

Neo-Freudians refer to a group of psychologists who, while influenced by the writings of Freud, expanded his theories to include social and cultural factors in personality development and dynamics.

Alfred Adler

An Austrian medical doctor, psychotherapist, and founder of the school of individual psychology known for his theories on the importance of feelings of inferiority.

Trait Theorists

Psychologists who study personality, focusing on the identification and classification of consistent behavioral patterns or traits.