Give an Appropriate Answer $\mathrm { f } ( \mathrm { x } , \mathrm { y } )$

question 392

Essay

Give an appropriate answer.
-Given the function $\mathrm { f } ( \mathrm { x } , \mathrm { y } )$ and the positive number $\varepsilon$ as in the formal definition of a limit, find a positive number $\delta$ as in the definition that insures $| f ( x , y ) - f ( 0,0 ) | < \varepsilon$ .
$f ( x , y ) = \frac { 2 x + y } { x ^ { 2 } y ^ { 2 } + 1 } ; \varepsilon = 0.12$

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Definitions:

Economic Loss

A monetary reduction in income, net worth, or value of assets beyond normal expectations, often as a result of business activities or economic policies.

Price

The amount of money required to purchase a good or service, determined by factors such as supply and demand.

Market Price

Market price is the current price at which a good or service can be bought or sold in a competitive marketplace.

Profit

The financial gain obtained when the amount of revenue gained from a business activity exceeds the expenses, costs, and taxes needed to sustain the activity.