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

question 48

Multiple Choice

Find
$$\lim _ { x \rightarrow 3 } [ g ( x ) - f ( x ) ]$$
for $f ( x ) = 3 x ^ { 3 }$ and $g ( x ) = \frac { \sqrt { x ^ { 2 } + 2 } } { 5 x ^ { 2 } }$ .

• A) \(\frac { \sqrt { 11 } } { 45 } - 81\)
• B) \(\frac { \sqrt { 3 } } { 5 } - 81\)
• C) \(\frac { 9 \sqrt { 11 } } { 5 }\)
• D) \(\frac { \sqrt { 3 } } { 5 } + 81\)
• E) limit does not exist

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Definitions:

General Adaptation Syndrome

A three-phase response pattern to stress described by Hans Selye, including alarm, resistance, and exhaustion stages.

Stress

The body's response to any demand or challenge, which can be physical, mental, or emotional in nature.

Acculturative Stress

The psychological impact of adapting to a new culture, which can include feelings of loss, confusion, and conflict between cultural norms.

Epinephrine

A hormone and neurotransmitter also known as adrenaline, involved in regulating heart rate, blood vessel and air passage diameters, and metabolic shifts; its release is crucial in the body's acute stress response.