At What Points Is the Given Function Continuous?
- $$f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 5 }$$

question 141

Multiple Choice

At what points is the given function continuous?
- $$f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 5 }$$

• A) All \(( x , y , z )\) such that \(x ^ { 2 } + y ^ { 2 } \neq 0\)
• B) All \(( x , y , z )\) such that \(x ^ { 2 } + y ^ { 2 } \neq 5\)
• C) All \(( x , y , z )\)
• D) All \(( x , y , z )\) such that \(x ^ { 2 } + y ^ { 2 } \neq 25\)

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Definitions:

Optimum

The condition or degree of an outcome that is most favorable or efficient for a specific purpose.

Maximize

To increase to the greatest possible amount or degree, often used in the context of optimizing performance, efficiency, or profits.

Iso-Profit Line

A graphical representation showing combinations of inputs that result in the same level of profit, used in economic and operational modeling.

Maximization Problem

A type of optimization problem that seeks the highest possible value of an objective function under given constraints.