Find the Value of the Limit $\lim _ { x \rightarrow 0 } \left( \frac { 1 } { x - 1 } - \frac { 1 } { \ln x } \right)$

question 240

Multiple Choice

Find the value of the limit $\lim _ { x \rightarrow 0 } \left( \frac { 1 } { x - 1 } - \frac { 1 } { \ln x } \right)$ .

• A)-1
• B) \(- \frac { 1 } { 2 }\)
• C)0
• D) \(\frac { 1 } { 2 }\)
• E)1
• F) \(\infty\)
• G) \(- \infty\)
• H)Does not exist

---

Definitions:

Drive Axle

A component of a vehicle's drivetrain that transfers power from the transmission to the wheels, enabling movement.

Differential Carrier

The housing that contains the differential gear set in a vehicle, supporting and protecting the gears as they adjust wheel speed during turns.

Crown and Pinion

A gear assembly in a vehicle's differential where the pinion (a small gear) engages with the crown (a larger gear) to allow wheels to rotate at different speeds.

Powerflow

The mechanical flow path that conducts motive power through a system or component. For instance, the powerflow through a transmission in a specific gear ratio would be the sequential routing of the torque flow path through those gears that are actually engaged.