Find the Potential Function F for the Field F $\mathbf { F } = \sec ^ { 2 } x \sin ^ { 2 } y \mathbf { i } + 2 \tan x \sin y \cos y \mathbf { j } + 8 z ^ { 7 } \mathbf { k }$

question 231

Multiple Choice

Find the potential function f for the field F.
- $\mathbf { F } = \sec ^ { 2 } x \sin ^ { 2 } y \mathbf { i } + 2 \tan x \sin y \cos y \mathbf { j } + 8 z ^ { 7 } \mathbf { k }$

• A) \(f ( x , y , z ) = \sec x \sin ^ { 2 } y + z + C\)
• B) \(f ( x , y , z ) = \tan x \sin ^ { 2 } y + z ^ { 8 } + C\)
• C) \(f ( x , y , z ) = \sec x \sin ^ { 2 } y + z ^ { 8 } + C\)
• D) \(f ( x , y , z ) = - \sec x \sin ^ { 2 } y + z ^ { 8 } + C\)

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Definitions:

Daily Basis

The frequency of something happening or being performed every day.

Progress Toward Adulthood

The process of developing attributes, skills, and experiences that mark the transition from childhood into adult roles and responsibilities.

Growth Spurt

A rapid increase in height and weight typically observed during adolescence due to hormonal changes.

Atypical Growth

Growth patterns that deviate from the expected or typical developmental trajectory.