$$\text { Use the linear approximation } ( 1 + x ) ^ { k } \approx 1 + k x \text {, as specified. }$$

question 428

Multiple Choice

$$\text { Use the linear approximation } ( 1 + x ) ^ { k } \approx 1 + k x \text {, as specified. }$$
-Find an approximation for the function $f ( x ) = ( 1 - x ) ^ { 5 }$ for values of $x$ near zero.

• A) \(f ( x ) \approx 1 + 6 x\)
• B) \(f ( x ) \approx 1 + 5 x\)
• C) \(f ( x ) \approx 5 + 5 x\)
• D) \(f ( x ) \approx 1 - 5 x\)

---

Definitions:

Producer Surplus

The gap between what sellers are prepared to accept for a product or service and the real amount they end up getting.

Excess Quantity

The situation where the supply of a product exceeds the demand for it at a specific price point, leading to a surplus.

Deadweight Loss

A loss of economic efficiency that can occur when the equilibrium for a good or a service is not achieved.

Market Equilibrium

The state in which the supply and demand for a good or service are balanced, leading to a stable price.