Find the Gradient Vector Field of the Function $f ( x , y ) = \ln \left( \sqrt { x ^ { 2 } + y ^ { 2 } } \right)$

question 100

Multiple Choice

Find the gradient vector field of the function $f ( x , y ) = \ln \left( \sqrt { x ^ { 2 } + y ^ { 2 } } \right)$ .

• A) \(\left( \frac { 2 x } { x ^ { 2 } + y ^ { 2 } } , \frac { 2 y } { x ^ { 2 } + y ^ { 2 } } \right)\)
• B)\(\left( \frac { x } { 2 \left( x ^ { 2 } + y ^ { 2 } \right) } , \frac { y } { 2 \left( x ^ { 2 } + y ^ { 2 } \right) } \right)\)
• C)\(\left( \frac { 1 } { x ^ { 2 } + y ^ { 2 } } , \frac { 1 } { x ^ { 2 } + y ^ { 2 } } \right)\)
• D)\(\left( \frac { 1 } { 2 \left( x ^ { 2 } + y ^ { 2 } \right) } , \frac { 1 } { 2 \left( x ^ { 2 } + y ^ { 2 } \right) } \right)\)
• E)\(\left( \frac { x } { x ^ { 2 } + y ^ { 2 } } , \frac { y } { x ^ { 2 } + y ^ { 2 } } \right)\)
• F)\(\left( \frac { - x } { x ^ { 2 } + y ^ { 2 } } , \frac { - y } { x ^ { 2 } + y ^ { 2 } } \right)\)
• G)\(\left( \frac { x } { x ^ { 2 } + y ^ { 2 } } , \frac { - y } { x ^ { 2 } + y ^ { 2 } } \right)\)
• H)\(\left( \frac { - x } { x ^ { 2 } + y ^ { 2 } } , \frac { y } { x ^ { 2 } + y ^ { 2 } } \right)\)

Identify the concepts and techniques involved in setting performance standards.

Recognize the principles of the control process, including the steps involved and their significance.

Understand the significance of involving employees in the goal-setting and objectives process.

Comprehend the concept and application of program evaluation and review technique (PERT), including critical path analysis.

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Definitions:

Phosphorus

A chemical element essential for life, involved in many cellular processes, including energy transfer and the formation of bones and teeth.

Biogeochemical Pathway

Cycles that involve the movement and chemical transformation of substances through biological, geological, and chemical processes on Earth.

Elements

Substances that cannot be broken down into substances with different properties; composed of only one type of atom.

Reservoir

Location in a biogeochemical cycle where a chemical or resource is stored for long periods of time and is typically unavailable to living organisms.