Find the Gradient Field of the Function A) $\bar { V } = ( 5 + 7 x ) x ^ { 4 } e ^ { 7 x _ { i } } + 3 y ^ { 2 } z ^ { 7 } j + 7 y ^ { 3 } z ^ { 6 } \mathbf { k }$

question 7

Multiple Choice

Find the gradient field of the function.
- $$\mathrm { f } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \mathrm { x } ^ { 5 } \mathrm { e } ^ { 7 \mathrm { x } } + \mathrm { y } ^ { 3 } \mathrm { z } ^ { 7 }$$

• A) \(\bar { V } = ( 5 + 7 x ) x ^ { 4 } e ^ { 7 x _ { i } } + 3 y ^ { 2 } z ^ { 7 } j + 7 y ^ { 3 } z ^ { 6 } \mathbf { k }\)
• B) \(\nabla = ( 1 + x ) x ^ { 4 } e ^ { 7 x _ { i } } + y ^ { 2 } z ^ { 7 } j + y ^ { 3 } z ^ { 6 } k\)
• C) \(\bar { A } = ( 5 + 7 x ) x ^ { 4 } e ^ { 7 x _ { i } } + 3 y ^ { 2 } j + 7 z ^ { 6 } \mathbf { k }\)
• D) \(\overline { \mathrm { f } } = ( 5 + 7 x ) \mathrm { x } ^ { 4 } \mathrm { e } ^ { 7 x _ { i } } + \left( \mathrm { x } ^ { 5 } \mathrm { e } ^ { 7 x } + 3 \mathrm { y } ^ { 2 } \mathrm { z } ^ { 7 } \right) \mathrm { j } + \left( \mathrm { x } ^ { 5 } \mathrm { e } ^ { 7 x } + 7 \mathrm { y } ^ { 3 } \mathrm { z } ^ { 6 } \right) \mathbf { k }\)

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Definitions:

Garcia

A reference likely to John Garcia, known for his research on taste aversion learning showing that an organism can learn to avoid a substance after a negative experience.

Operant Conditioning

An approach to learning where behaviors are influenced to be repeated or not through the administration of punishments and rewards.

Self-modification

The process of changing one's behavior or characteristics by oneself, often with the aim of improving personal well-being.

Systematically Reward

The process of providing rewards or reinforcements in a planned and consistent manner to encourage specific behavior.