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:

Capital

Long-term assets or the money used to support long-term assets and projects. Long-term debt and equity on the balance sheet.

Profitability Index

A capital budgeting tool that measures the relationship between the present value of cash inflows and the initial investment, indicating the relative profitability of a project.

Cost of Capital

The rate of return a company must earn on its projects to maintain its market value and attract funding, often consisting of debt and equity costs.

Cash Flows

The aggregate sum of funds moving into and out of a company, particularly influencing its liquidity.