Find the Potential Function F for the Field F $$\mathbf { F } = - \frac { 1 } { x } \mathbf { i } + \frac { 1 } { \mathrm { y } } \mathrm { j } - \frac { 1 } { \mathrm { z } } \mathbf { k }$$

question 22

Multiple Choice

Find the potential function f for the field F.
- $$\mathbf { F } = - \frac { 1 } { x } \mathbf { i } + \frac { 1 } { \mathrm { y } } \mathrm { j } - \frac { 1 } { \mathrm { z } } \mathbf { k }$$

• A) \(f ( x , y , z ) = \frac { 1 } { x ^ { 2 } } - \frac { 1 } { y ^ { 2 } } + \frac { 1 } { z ^ { 2 } } + C\)
• B) \(f ( x , y , z ) = \ln ( y - x - z ) + C\)
• C) \(f ( x , y , z ) = \ln \left( \frac { y } { x z } \right) + C\)
• D) \(f ( x , y , z ) = \frac { 1 } { x ^ { 2 } y ^ { 2 } z ^ { 2 } } + C\)

---

Definitions:

Tax Increase

An escalation in the statutory rate imposed by the government on income, goods, services, or transactions.

Tariff Rates

Taxes imposed on imported goods and services, which can affect the price and availability of those goods and services.

Expansionary Policies

Economic strategies implemented by a government or central bank to spur economic growth, typically through increased government spending or reduced taxes.

Economic Downturn

A period of reduced economic activity characterized by declining GDP, unemployment, and falling prices.