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) \(984 \pi\)

Understand personal projects or strivings as forms of goals and their influence on personal achievement.

Comprehend the concept of self-determination theory and its applications to autonomy and motivation.

Recognize the importance of goal hierarchies and the process of achieving long-term goals through intermediate steps.

Grasp the concept of the planning fallacy and its effects on goal setting and achievement.

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Definitions:

Self-Serving Bias

The common tendency to attribute one's successes to personal characteristics and one's failures to external factors.

Angry When Criticized

A behavioral response where individuals display anger or irritation in response to criticism, reflecting a possible sensitivity to negative feedback.

Ambiguous and Confusing

Descriptions or situations that are unclear, open to more than one interpretation, and cause confusion.

Self-Serving Bias

A cognitive bias where individuals attribute positive outcomes to their own actions or characteristics, and negative outcomes to external factors.