Find the Domain and Range and Describe the Level Curves $$f ( x , y ) = \frac { 1 } { 4 x ^ { 2 } + 5 y ^ { 2 } }$$

question 390

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
- $$f ( x , y ) = \frac { 1 } { 4 x ^ { 2 } + 5 y ^ { 2 } }$$

• A) Domain: all points in the \(x y\)-plane except \(( 0,0 )\); range: all real numbers; level curves; ellipses \(4 x ^ { 2 } + 5 y ^ { 2 } = c\)
• B) Domain: all points in the xy-plane except \(( 0,0 )\); range: real numbers \(> 0\); level curves: ellipses \(4 x ^ { 2 } + 5 y ^ { 2 } = c\)
• C) Domain: all points in the \(x y\)-plane; range: all real numbers; level curves; ellipses \(4 x ^ { 2 } + 5 y ^ { 2 } = c\)
• D) Domain: all points in the \(x y\)-plane; range: real numbers \(> 0\); level curves: ellipses \(4 x ^ { 2 } + 5 y ^ { 2 } = c\)

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Definitions:

Equivalent Units

A concept used in cost accounting to represent the amount of work done on incomplete units, translated into the amount of completed units.

Conversion Costs

Conversion costs are the costs incurred to convert raw materials into finished products, including direct labor and manufacturing overhead expenses.

Conversion Costs

Costs related to turning raw materials into finished goods, typically including labor and manufacturing overhead expenses.

Materials Costs

Expenses incurred in the acquisition of raw materials used in production.