Find an Upper Bound for the Magnitude |E| of the Error

question 301

Multiple Choice

Find an upper bound for the magnitude |E| of the error in the approximation f(x, y) ≈ L(x, y) at the given point over the
given region R.
- $$f ( x , y ) = - 4 x ^ { 2 } + 9 y ^ { 2 } - 9 \text { at } ( - 3 , - 2 ) ; R : | x + 3 | \leq 0.1 , | y + 2 | \leq 0.1$$

• A) \(| E | \leq 0.18\)
• B) \(| E | \leq 0.27\)
• C) \(| E | \leq 0.36\)
• D) \(| E | \leq 0.09\)

---

Definitions:

Economic Profit

The total revenue minus total costs, including both explicit and implicit costs.

Competitive Market

A market structure characterized by a large number of sellers and buyers, where no single party can dictate prices or market conditions.

Price-Taker Industry

An industry in which individual firms have no control over the price set by the market and must accept the prevailing price.

Total Revenues

The total income received by a firm from selling its goods or services before any costs or expenses are subtracted.