Give an Appropriate Answer $f ( x , y , z )$

question 56

Essay

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

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Definitions:

Process Innovation

The implementation of a new or significantly improved production or delivery method in a business or industry.

Product Innovation

The process of developing and introducing new or significantly improved products to the market, enhancing variety, performance, or quality.

Invention

The creation of a new product, process, or method that has never been made before, through the use of imagination and ingenuity.

Imitation

is the action of using someone or something as a model and attempting to replicate their success or characteristics.