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:

Auditory Stimulus

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Manic Episode

A period of abnormally elevated or irritable mood, heightened energy, and activity levels, often associated with bipolar disorder.