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

question 204

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 $| f ( x , y , z ) - f ( 0,0,0 ) | < \varepsilon$ .
$f ( x , y , z ) = \frac { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } { x + 1 } ; \varepsilon = 0.03$

---

Definitions:

Marginal Utility

The extra pleasure a customer receives from consuming an additional unit of a product or service.

Total Utility

The total satisfaction received by consuming a particular amount of goods or services.

Utility

The total satisfaction received from consuming a good or service.