Using the Divergence Theorem, Find the Outward Flux of F $\mathbf { F } = 2 \mathrm { x } ^ { 3 } \mathbf { i } + 2 \mathrm { y } ^ { 3 } \mathrm { j } + 2 \mathrm { z } ^ { 3 } \mathbf { k }$

question 138

Multiple Choice

Using the Divergence Theorem, find the outward flux of F across the boundary of the region D.
- $\mathbf { F } = 2 \mathrm { x } ^ { 3 } \mathbf { i } + 2 \mathrm { y } ^ { 3 } \mathrm { j } + 2 \mathrm { z } ^ { 3 } \mathbf { k }$ ; D: the thick sphere $16 \leq \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } \leq 25$

• A) \(\frac { 50424 } { 5 } \pi\)
• B) \(366 \pi\)
• C) \(50,424 \pi\)
• D) \(984 \pi\)

---

Definitions:

SWOT Analysis

A strategic planning tool used to identify Strengths, Weaknesses, Opportunities, and Threats related to business competition or project planning.

Core Competencies

refer to the unique strengths and abilities that a company or individual possesses, which give them a competitive advantage in the market.

Special Strengths

Unique abilities or talents that distinguish an individual or entity from others; often contributing significantly to success.

Leader

An individual who guides or influences a group towards achieving goals or objectives, often demonstrating authority or inspiration.