Find the Curl of the Vector Field F $\mathbf { F } ( x , y , x ) = 3 y z ^ { 3 } \mathbf { i } + 8 x ^ { 5 } y ^ { 4 } \mathbf { j } + 4 x \mathbf { k }$

question 32

Multiple Choice

Find the curl of the vector field F. $\mathbf { F } ( x , y , x ) = 3 y z ^ { 3 } \mathbf { i } + 8 x ^ { 5 } y ^ { 4 } \mathbf { j } + 4 x \mathbf { k }$

• A) \(32 x ^ { 5 } y ^ { 3 }\)
• B) \(32 x ^ { 5 } y ^ { 3 } \mathbf { j }\)
• C) \(9 y z ^ { 2 } + 40 x ^ { 4 } y ^ { 4 } - 3 z ^ { 3 } - 4\)
• D) \(\left( 9 y z ^ { 2 } - 4 \right) \mathbf { j } + \left( 40 x ^ { 4 } y ^ { 4 } - 3 z ^ { 3 } \right) \mathbf { k }\)

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Definitions:

Limiting Factor

An environmental condition that restricts the growth, abundance, or distribution of an organism or a population within an ecosystem.

Terrestrial Ecosystems

are ecosystems found on land, characterized by diverse biotic communities interacting with the abiotic environment.

Precipitation

Any form of water, liquid or solid, that falls from the atmosphere and reaches the ground.

Biotic Factor

A living component of an ecosystem, such as plants, animals, and microorganisms, that affects and interacts with other organisms in their environment.