Participation Activity #3This Is Similar To Try It #3 In The OpenStax Text.Complete The Following Table For $f(x) = \frac{24 \sin X}{4 X}$, Then Estimate The Limit Of The Function As $x$ Approaches 0.Round Your Answers In The Table

Participation Activity #3: Exploring the Limit of a Trigonometric Function

In this participation activity, we will explore the limit of a trigonometric function as x approaches 0. We will complete a table of values for the function f(x) = \frac{24 \sin x}{4 x} and use the data to estimate the limit of the function.

The function we will be working with is f(x) = \frac{24 \sin x}{4 x}. This function involves the sine function and a rational expression. We will need to evaluate the function at various values of x to complete the table.

To complete the table, we will evaluate the function f(x) = \frac{24 \sin x}{4 x} at various values of x. We will round our answers to 4 decimal places.

To evaluate the function f(x) = \frac{24 \sin x}{4 x}, we will use a calculator or computer to find the values of the function at the given values of x.

Now that we have completed the table, we can use the data to estimate the limit of the function as x approaches 0. Looking at the table, we can see that the values of the function are getting closer and closer to 0.6 as x approaches 0.

In this participation activity, we explored the limit of a trigonometric function as x approaches 0. We completed a table of values for the function f(x) = \frac{24 \sin x}{4 x} and used the data to estimate the limit of the function. Our results suggest that the limit of the function as x approaches 0 is approximately 0.6.

1. What is the limit of the function f(x) = \frac{24 \sin x}{4 x} as x approaches 0?
2. How did you use the table of values to estimate the limit of the function?
3. What would happen if we were to evaluate the function at x = 0?
4. How does the limit of the function relate to the behavior of the sine function as x approaches 0?

• OpenStax: Try it #3
• Khan Academy: Limits of trigonometric functions
• Wolfram Alpha: Limit of a trigonometric function

• Complete the table of values for the function f(x) = \frac{24 \sin x}{4 x} and use the data to estimate the limit of the function.
• Answer the discussion questions.
• Evaluate the function at x = 0 and explain the result.
• Research and discuss the relationship between the limit of the function and the behavior of the sine function as x approaches 0.
  Participation Activity #3: Exploring the Limit of a Trigonometric Function - Q&A

In this Q&A article, we will continue to explore the limit of a trigonometric function as x approaches 0. We will answer some common questions related to the topic and provide additional resources for further learning.

A: The limit of the function f(x) = \frac{24 \sin x}{4 x} as x approaches 0 is approximately 0.6. This can be seen from the table of values we completed earlier.

A: We used the table of values to estimate the limit of the function by looking at the behavior of the function as x approaches 0. As x gets closer and closer to 0, the values of the function get closer and closer to 0.6.

A: If we were to evaluate the function at x = 0, we would get an undefined result. This is because the function is not defined at x = 0.

A: The limit of the function f(x) = \frac{24 \sin x}{4 x} as x approaches 0 is related to the behavior of the sine function as x approaches 0. As x gets closer and closer to 0, the sine function approaches 0. This is because the sine function is an odd function, and as x approaches 0, the sine function approaches 0.

A: The limit of the function f(x) = \frac{24 \sin x}{4 x} as x approaches 0 is significant because it helps us understand the behavior of the function as x approaches 0. This is important in many areas of mathematics and science, such as calculus and physics.

A: There are many resources available to learn more about limits of trigonometric functions. Some of these resources include:

• OpenStax: Try it #3
• Khan Academy: Limits of trigonometric functions
• Wolfram Alpha: Limit of a trigonometric function
• Calculus textbooks and online resources

A: Some common mistakes to avoid when working with limits of trigonometric functions include:

• Not using the correct definition of the limit
• Not evaluating the function at the correct value of x
• Not considering the behavior of the function as x approaches 0
• Not using the correct notation and terminology

In this Q&A article, we have answered some common questions related to the limit of a trigonometric function as x approaches 0. We have also provided additional resources for further learning and discussed some common mistakes to avoid when working with limits of trigonometric functions.

1. What is the limit of the function f(x) = \frac{24 \sin x}{4 x} as x approaches 0?
2. How did you use the table of values to estimate the limit of the function?
3. What would happen if we were to evaluate the function at x = 0?
4. How does the limit of the function relate to the behavior of the sine function as x approaches 0?

• OpenStax: Try it #3
• Khan Academy: Limits of trigonometric functions
• Wolfram Alpha: Limit of a trigonometric function
• Calculus textbooks and online resources

• Answer the discussion questions.
• Evaluate the function at x = 0 and explain the result.
• Research and discuss the relationship between the limit of the function and the behavior of the sine function as x approaches 0.