Find $$\lim _ { x \rightarrow 3 } [ g ( x ) - f ( x ) ]$$

question 111

Multiple Choice

Find
$$\lim _ { x \rightarrow 3 } [ g ( x ) - f ( x ) ]$$
for $f ( x ) = 3 x ^ { 3 }$ and $g ( x ) = \frac { \sqrt { x ^ { 2 } + 2 } } { 6 x ^ { 2 } }$ .

• A) \(\frac { \sqrt { 11 } } { 54 } - 81\)
• B) \(\frac { \sqrt { 3 } } { 6 } - 81\)
• C) \(\frac { 3 \sqrt { 11 } } { 2 }\)
• D) \(\frac { \sqrt { 3 } } { 6 } + 81\)
• E) limit does not exist

---

Definitions:

Chess and Thomas

Researchers known for their contributions to developmental psychology, particularly in the study of temperament in children.

Temperament

Refers to the innate characteristics of an individual's personality, including tendencies toward emotional reactivity, intensity, and sociability.

Behavioral Style

The characteristic way in which an individual reacts and interacts with the environment, often consistent across different situations.

Personal Responsibility

The idea that individuals are accountable for their own actions and wellbeing, including taking charge of their life decisions and accepting the consequences.