Give an Appropriate Answer $f ( x , y )$ And the Positive Number

question 382

Essay

Give an appropriate answer.
-Given the function $f ( x , y )$ and the positive number $\varepsilon$ as in the formal definition of a limit, find a positive number $\delta$ as in the definition that insures $| \mathrm { f } ( \mathrm { x } , \mathrm { y } ) - \mathrm { f } ( 0,0 ) | < \varepsilon$ .
$f ( x , y ) = ( 1 + \cos x ) ( x + y ) ; \varepsilon = 0.08$

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Definitions:

Habitual Purchasers

Consumers who buy the same products or services regularly, often out of routine or loyalty, rather than conscious decision-making.

Store Loyalty

The tendency of customers to continue shopping at the same store or brand rather than switching to competitors.

Temporal State

Refers to the condition or state of something at a specific time, often used in psychology to describe how timing affects human behavior and decision-making.

Behavioral Component

A component of attitude that comprises the actions a person takes with regard to the issue at hand.