Choose the One Alternative That Best Completes the Statement or Answers

question 102

Multiple Choice

Choose the one alternative that best completes the statement or answers the question.
Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
- $$\frac { 7 x ^ { 5 } + 5 x ^ { 3 } + 7 x ^ { 2 } + 6 } { x ( x - 5 ) ^ { 3 } \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }$$

• A) \(\frac { A } { x } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { ( x - 5 ) ^ { 3 } } + \frac { E x } { x ^ { 2 } + 2 x + 5 } + \frac { F x } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }\)
• B) \(\frac { A } { x } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { ( x - 5 ) ^ { 3 } } + \frac { E } { x ^ { 2 } + 2 x + 5 } + \frac { F } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }\)
• C) \(\frac { A } { x } + \frac { B } { x - 5 } + \frac { C } { ( x - 5 ) ^ { 2 } } + \frac { D } { ( x - 5 ) ^ { 3 } } + \frac { E x + F } { x ^ { 2 } + 2 x + 5 } + \frac { G x + H } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }\)
• D) \(\frac { A } { x } + \frac { B } { ( x - 5 ) ^ { 3 } } + \frac { C x + D } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } }\)

---

Definitions:

Implicit Costs

Costs that represent forgone opportunities, often not directly outlaid but incurred when resources are used for one purpose over another.

Marginal Cost

captures the cost added by producing one extra item of a product, emphasizing the concept of economies of scale and efficiency in production.

Marginal Product

An increase in output resulting from the use of one more unit of a particular input, holding all other inputs constant.

Opportunity Costs

The price paid when one skips the second-best option available in making a choice.