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 $| f ( x , y , z ) - f ( 0,0,0 ) | < \varepsilon$ .
$f ( x , y , z ) = \sin ^ { 2 } x + \sin ^ { 2 } y + \sin ^ { 2 } z ; \varepsilon = 0.12$

---

Definitions:

Epithelial Tissues

Layers of cells that cover the body's surfaces, line cavities, and form glands, playing key roles in protection, secretion, and absorption.

Sweating

The process of secreting fluid from the body's sweat glands, primarily for cooling the body through evaporation.

Panting

Rapid shallow breathing through the mouth, often used as a means of reducing body temperature by animals, including humans.

Muscle Activity

The physical action or movement produced by the contraction of muscles, which can be voluntary or involuntary, playing a critical role in posture, movement, and circulation.