Using the Divergence Theorem, Find the Outward Flux of F $\mathbf { F } = \mathrm { e } ^ { \mathrm { yz } } \mathrm { i } + 6 \mathrm { yj } + 8 \mathrm { z } ^ { 2 } \mathbf { k } ;$

question 137

Multiple Choice

Using the Divergence Theorem, find the outward flux of F across the boundary of the region D.
- $\mathbf { F } = \mathrm { e } ^ { \mathrm { yz } } \mathrm { i } + 6 \mathrm { yj } + 8 \mathrm { z } ^ { 2 } \mathbf { k } ;$ D: the solid sphere $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } \leq 64$

• A) \(12,288 \pi\)
• B) \(36864 \pi\)
• C) \(4096 \pi\)
• D) \(\frac { 2048 } { 3 } \pi\)

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Definitions:

Motor Development

The progression of muscle coordination and movement abilities in individuals, especially during the early years of life.

Gesell

Refers to Arnold Gesell, an American psychologist and pediatrician known for his work in child development.

Maturation

The process of becoming mature, encompassing growth and development in physical, intellectual, or emotional capabilities.

Dynamic Systems View

A theoretical perspective proposing that development is a complex process, resulting from the interaction of various systems within the individual and their environment.