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

question 360

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 $| \mathrm { f } ( \mathrm { x } , \mathrm { y } ) - \mathrm { f } ( 0,0 ) | < \varepsilon$ .
$f ( x , y ) = \frac { x + y } { x ^ { 2 } + y ^ { 2 } + 1 } ; \varepsilon = 0.06$

---

Definitions:

Net Present Value

A method used in capital budgeting to evaluate the profitability of an investment by calculating the difference between the present value of cash inflows and outflows over a period of time.

Internal Rate of Return

A metric used in financial analysis to estimate the profitability of potential investments.

Time Value of Money

The concept that money available today is worth more than the same amount in the future due to its potential earning capacity.

Capital Investment Project

A project undertaken by a business to acquire or upgrade physical assets such as property, industrial buildings, or equipment to create future benefits.