Use L'Hopital's Rule to Evaluate the Limit $\lim _ { x \rightarrow \frac { \pi } { 3 } } \frac { \cos x - \frac { 1 } { 2 } } { x - \frac { \pi } { 3 } }$

question 12

Multiple Choice

Use l'Hopital's Rule to evaluate the limit.
- $\lim _ { x \rightarrow \frac { \pi } { 3 } } \frac { \cos x - \frac { 1 } { 2 } } { x - \frac { \pi } { 3 } }$

• A) \(- \sqrt { 3 }\)
• B) \(\frac { \sqrt { 3 } } { 2 }\)
• C) \(\frac { \sqrt { 2 } } { 2 }\)
• D) \(- \frac { \sqrt { 3 } } { 2 }\)

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Definitions:

Difference Thresholds

The minimum difference in stimulation that a person can detect 50 percent of the time, also known as the just noticeable difference (JND).

Absolute Thresholds

The minimum stimulus intensity required to be perceptible to the senses.

Sensory Adaptation

The process by which sensory receptors become less sensitive to constant stimuli over time, reducing our awareness of them.

Subliminal Persuasion

A method of influence that operates below the level of conscious awareness, where stimuli are used to affect an individual's thinking or behavior without them being aware of it.