Find the Gradient Vector Field of the Function $f ( x , y , z ) = x \sin y + z ^ { 2 }$

question 216

Multiple Choice

Find the gradient vector field of the function $f ( x , y , z ) = x \sin y + z ^ { 2 }$ .

• A) \(\sin y \mathbf { i } + \cos y \mathbf { j } + 2 \mathbf { k }\)
• B) \(\sin y \mathbf { i } + x \cos y \mathbf { j } + 2 z \mathbf { k }\)
• C)\(x \sin y \mathbf { i } + \cos y \mathbf { j } + \mathbf { k }\)
• D) \(x \sin y \mathbf { i } + x \cos y \mathbf { j } + 2 z \mathbf { k }\)
• E)\(\sin y \mathbf { i } - \cos y \mathbf { j } - 2 \mathbf { k }\)
• F)\(\sin y \mathbf { i } - x \cos y \mathbf { j } + z \mathbf { k }\)
• G)\(x \sin y \mathbf { i } - \cos y \mathbf { j } + z \mathbf { k }\)
• H)\(x \sin y \mathbf { i } - x \cos y \mathbf { j } + z \mathbf { k }\)

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Definitions:

Deposited

Placing money into a financial account or institution for safekeeping or to earn interest.

IRA

Individual Retirement Account, a saving account with tax advantages that individuals can use to save and invest long-term.

Compounded Annually

The process of calculating interest on both the initial principal and the accumulated interest from previous periods once a year.

Retirement

The point in time when an individual chooses to leave the workforce permanently, often accompanied by receiving pension or retirement savings.