Use Taylor's Formula to Find the Requested Approximation of F(x $10 x + y - 50 x ^ { 2 } - 5 x y - \frac { 1 } { 2 } y ^ { 2 }$

question 213

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Quadratic approximation to f(x, y) = ln(1 + 10x + y)

• A) \(10 x + y - 50 x ^ { 2 } - 5 x y - \frac { 1 } { 2 } y ^ { 2 }\)
• B) \(1 + 10 x + y - 50 x ^ { 2 } - 5 x y - \frac { 1 } { 2 } y ^ { 2 }\)
• C) \(1 + 10 x + y - 50 x ^ { 2 } - 10 x y - \frac { 1 } { 2 } y ^ { 2 }\)
• D) \(10 x + y - 50 x ^ { 2 } - 10 x y - \frac { 1 } { 2 } y ^ { 2 }\)

---

Definitions:

Total Variable Cost

The sum of all costs that vary with the level of output, such as raw materials and labor expenses, for a given period.

Average Variable Cost (AVC)

The total variable costs of production divided by the quantity of output produced, representing the variable cost per unit of output.

Average Total Cost

The total cost of production divided by the quantity of output produced, representing the average cost per unit of good or service.

Average Fixed Cost

The fixed costs of production (costs that do not change with output) divided by the quantity of output produced, which decreases as production increases.