Find Two Paths of Approach from Which One Can Conclude

question 76

Multiple Choice

Find two paths of approach from which one can conclude that the function has no limit as (x, y) approaches (0, 0) .
- $\text { Define } f ( 0,0 ) \text { in a way that extends } f ( x , y ) = \frac { 6 x ^ { 2 } - x ^ { 2 } y + 6 y ^ { 2 } } { x ^ { 2 } + y ^ { 2 } } \text { to be continuous at the origin. }$

• A) f(0, 0) = 0
• B) f(0, 0) = 6
• C) f(0, 0) = 2
• D) f(0, 0) = 12

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Definitions:

Profit-Maximizing Level

The specific output level at which a business achieves its maximum profit, determined through analysis of costs and revenues.

Output

The quantity of goods or services produced by a firm, industry, or economy in a given period.

Marginal Cost

The change in total production cost that comes from making or producing one additional unit.

Total Cost

The total amount of money spent on creating goods or services, encompassing both constant and fluctuating expenses.