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:

Sampling Distribution

The pattern of probability distribution associated with a particular statistic, derived from a random sample.

Normal Curve

A type of continuous probability distribution for a real-valued random variable, characterized by its bell-shaped curve that is symmetrical around its mean.

Normal Curve

A bell-shaped curve that represents the distribution of a dataset where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions.

Binomial Probability

The probability of achieving a specific number of successes in a fixed number of independent trials, each with the same probability of success.