Determine the Continuity of the Function $$f ( x , y , z ) = \frac { 5 z } { x ^ { 2 } + y ^ { 2 } - 3 }$$

question 22

Multiple Choice

Determine the continuity of the function $$f ( x , y , z ) = \frac { 5 z } { x ^ { 2 } + y ^ { 2 } - 3 }$$

• A) continuous except at \(( 0,0 )\)
• B) continuous for \(x ^ { 2 } + y ^ { 2 } = 3\)
• C) continuous except at \(( 5,0 )\)
• D) continuous except at \(( 0,3 )\)
• E) continuous for \(x ^ { 2 } + y ^ { 2 } \neq 3\)

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Definitions:

Unregulated Monopolist

A single seller in a market without government controls, setting prices and output levels at will to maximize profits.

Maximize Profits

The objective of most private firms to increase their bottom line to the highest possible level given their resources and market conditions.

Natural Monopolies

A market condition where due to high infrastructure costs or significant barriers to entry, a single company can supply a product or service more efficiently than multiple competing firms.

Government Regulation

The establishment of rules and laws by government bodies that are intended to control or govern conduct and practices within various sectors.